The figure shows a person estimating the height of a tree by looking at the
top of the tree with a mirror. Assuming that both the person and the tree form
right angles with the ground, which of the following proportions can be used
to estimate the height of the tree?

The Figure Shows A Person Estimating The Height Of A Tree By Looking At Thetop Of The Tree With A Mirror.

Answers

Answer 1

Answer:

The proportion that can be used to estimate the height of the tree is option;

A. [tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex]

Step-by-step explanation:

The given parameters in the question are;

The medium through which the person looks at the top of the tree = A mirror

The angle formed by the person and the tree with the ground = Right angles = 90°

The distance of the person from the mirror, d₁ = 5 ft.

The height of the person, h₁ = 6 ft.

The distance of the tree from the mirror, d₂ = 12 ft.

The angle formed by the incident light from the tree on the mirror, θ₁ = The angle of the reflected light from the mirror to the person, θ₂

Let 'A', 'B', 'M', 'T', and 'R' represent the location of the point at the top of the person's head, the location of the point at the person's feet, the location of the mirror, the location of the top of the tree and the location of the root collar of the tree, we have;

TR in ΔMRT = The height of the tree = h, and right triangles ΔABM and ΔMRT are similar

The corresponding legs are;

The height of the person and the height of the tree, which are AB = 6 ft. and TR = h, respectively

The distances of the person and the tree from the mirror, which are BM = 5 ft. and MR = 12 ft. respectively

∴ The angle formed by the incident light from the tree on the mirror, θ₁ = ∠TMR

The angle of the reflected light from the mirror to the person, θ₂ = ∠AMB

Given that θ₁ = θ₂, we have;

tan(θ₁) = tan(θ₂)

∴ tan(∠TMR) = tan(∠AMB)

[tex]tan\angle X = \dfrac{Opposite \ leg \ length \ to \ reference \ angle}{Adjacent \ leg \ length \ to \ reference \ angle}[/tex]

[tex]tan(\angle TMR) = \dfrac{TR}{MR} = \dfrac{h}{12}[/tex]

[tex]tan(\angle AMB) = \dfrac{AB}{BM} = \dfrac{6}{5}[/tex]

From tan(∠TMR) = tan(∠AMB), we have;

[tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex]

[tex]\therefore h = \dfrac{6 \, ft.}{5 \, ft.} \times 12 \, ft. = 14.4 \, ft.[/tex]

The height of the tree, h = 14.4 ft.

Therefore, from the proportion [tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex] the height of the tree can be estimated.


Related Questions

PLEASE HELP ASAP WILL MARK BRAINLIEST

what is the area of this trapezoid?

Answers

Answer:

10.5 units²

Step-by-step explanation:

Area of trapezoid = ½(a + b)h

where,

a = SK = 2 units

b = OC = 5 units

h = SO = 3 units

Plug in the values

Area = ½(2 + 5)*3

Area = ½(7)*3

Area = 10.5 units²

How do I shift the function a(x)=|x|+3 2 units to the right to the right. This is due today please help

Answers

Answer:

QUESTION:

How do I shift the function a(x)=|x|+3 2 units to the right?

ANSWER:

Try Math___way I always go there for help when no one can help me here. Just type in your math question and you get instant answers and an explanation.

Step-by-step explanation:

Hope that this helps you out! :)        

If you have any questions please put them in the comment section below this answer.        

Have a great rest of your day/night!        

Please thank me on my profile if this answer has helped you.

Compare investing $1500 at 9% compounded monthly for 11 years with investing $1500 at 14% compounded monthly for 11 years.

Answers

Answer:

Final amount after 11 years = $4021.97

Step-by-step explanation:

We will use the formula to get the final amount after t years,

Final amount = [tex]a(1+\frac{r}{n})^{nt}[/tex]

here a = Initial amount

r = Rate of interest

n = Number of compounding in a year

For Initial amount 'a' = $1500

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You are a business developer and charge $45 for a site visit plus additional $24 per hour for each hour you spend training employees. Write and solve an equation to determine how many total hours you have to work to earn $810 working hours at two separate businesses.

Answers

Answer: [tex]28.3\ hr[/tex]

Step-by-step explanation:

Given

Charge of the site visit [tex]\$45[/tex]

Additional charge per hour is [tex]\$24\ \text{per hour}[/tex]

He eaned [tex]\$810[/tex]

Suppose he worked for x hours

[tex]\therefore 810=45+24x\\\text{On solving}[/tex]

[tex]\Rightarrow 765=24x\\\Rightarrow x=28.3\ hr[/tex]

There plz help me is my last question and assignment

Answers

Answer:

I believe Jamal is correct, because he is just doing it an easy way. Instead of converting the mixed number to an improper fraction he is adding the measurements step by step.

Hope it Helps!

:)

please help meeeeeeeeeeeeee

Answers

wine distributors, they are sales men of wine

Will give extra points if you get it right <3

Add or subtract the given polynomials. Be sure to show all steps
(9x2 + 3x – 5) + (8x2 – x + 2)

Answers

Answer:

17x² + 2x – 3

Step-by-step explanation:

(9x2 + 3x – 5) + (8x2 – x + 2) →

(9x² + 3x – 5) + (8x² – x + 2) →

[Group like terms]

(9x² + 8x²) + (3x – x) + (2 – 5) →

[Simplify]

17x² + 2x – 3

Write the number in standard form.
5 x 10^2

Answers

Answer:

500 would be the answer of this question but it is also the standard form of this question

OK THIS IS NOT LIKE A SCHOOL QUESTION. But I play softball and I have long acrylic am i gonna
Get like kicked off the team or like in trouble for having them..?

Answers

Answer:

I don't know but if it feels like you shouldn't be doing it then don't

Step-by-step explanation:

Answer:

You won't get in huge trouble but it probably wouldn't be the smartest thing to have them. if you think you can play good with them then you are fine! you should double check with the coach, because every school or team has different rules!

istg this is ez sh.it but im a dum.b wh0re so give an explanation and i'll give you a cookie :)

Answers

Answer:

G

Step-by-step explanation:

when x is inputed it will give only one answer.

comparing rational and irrational numbers page 26 of spectrum math​

Answers

Answer:123456780-0987654321234567876543212345676543212

Step-by-step explanation:UGLY FAT Pig took 5000 kids in his basement and he ate them but they were fake kids and they were bombs and he heard the beep bep beep sound but instead of beep it was ugly fat pig and he die this is your only right answer

Answer:

Irrational means you have a never ending number such as 8.90919273788..... A rational number means it ends such as 36 or 5.113

please help! :) I need the answer quick

Answers

Answer:no clue

Step-by-step explanation:

i need the points im sorry

Answer:

x ≈ 2.3

Step-by-step explanation:

Given

x³ = 12 ( take the cube root of both sides )

x = [tex]\sqrt[3]{12}[/tex] ≈ 2.3 ( to 1 dec. place )

In ΔRST, r = 620 inches, s = 840 inches and t=230 inches. Find the area of ΔRST to the nearest square inch.

Answers

Answer:

24179 square inches

Step-by-step explanation:

In ΔRST, r = 620 inches, s = 840 inches and t=230 inches. Find the area of ΔRST to the nearest square inch.

We use the formula

Heron's formula = √s(s - a)(s - b)(s - c)

Where s = a + b + c/2

Solving for s

s = 620 + 840 + 230/2

s = 845

Solving for the area of the triangle

= √845 × (845 - 620) × (845 - 840) × (845 - 230)

= √584634375

= 24,179.213696893 square inches

Approximately = 24179 square inches

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Answers

X=23 because all the angles added together need to add to 180 (I would recommend asking your teacher for help to make sure you fully understand this concept)

find the median of the table below. Number of inches 20,22,24,26. Frequency 3,2,1,3. ​

Answers

Answer:

23

Step-by-step explanation:

20,22,24,26

(22+24)/2 = 23

Hope this helps my bad if its wrong

The middle value of the data set in the table given, which is the median, is: 22.

What is the Median of a Data Set?

The middle value of an ordered data set is the median of the data, which is also called the center of the data set.

Given the table, the middle value is the 5th data point, which lies at 22.

Therefore, the median of the data in the table is: 22.

Learn more about median of a data on:

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what is the distance of the dog along the coordinate number line​

Answers

Answer:

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Step-by-step explanation:

Theo deposits $3,000 in a savings account earning compound interest at an annual rate of 3% compounded annually. He makes no additional deposits or withdrawals. Use the formula for compound interest to find the amount in the account after 10 years.

After 10 years, there will be $____
in the account.

Answers

Answer:

$4031.75

Step-by-step explanation:

Amt after 10 years = 3000(1 + 0.03)^10

= 4031.749


A lumber company had 4 bundles of wood (12 pieces total). What is the rate of pieces per
bundle?

Answers

Answer:

There are three pieces per bundle.

Write the equation in standard form for a circle that has a diameter with endpoints (8,0) and (-8,0)

Answers

Answer:

x²+y² = 64

Step-by-step explanation:

The standard form of writing the equation of a circle is expressed as;

(x-a)²+(y-b)² = r² where;

(a, b) is the centre of the circle

r is the radius of the circle

Given the diameter of the circle with endpoints (8,0) and (-8, 0)

d = √(x2-x1)²+(y2-y1)²

d = √(-8-8)²+(0-0)²

d = √(-16)²

d = √256

d = 16

radius r = 16/2

r = 8

The centre of the circle will be the midpoint of the coordinates

M = (8-8/2, 0+0/2)

M = (0/2, 0/2)

M = (0,0)

Hence the centre is at (0,0)

Get the required equation

Recall that (x-a)²+(y-b)² = r²

Substitute the centre and the radius

(x-0)²+(y-0)² = 8²

x²+y² = 64

This gives the required equation

Lu is graphing the ordered pair (3,5). Starting at the origin, what does she
need to do? *
A. Move 3 units up and 5 units to the right, and draw a dot at that point.
B. Move 3 units up and 3 units to the right, and draw a dot at that point.
O
C. Move 3 units to the right and 5 units up, and draw a dot at that point.
D. Move 5 units to the right and 3 units up, and draw a dot at that point.

Answers

Answer:

C. Move 3 units to the right and 5 units up, and draw a dot at that point.

Step-by-step explanation:

My YT is YoungGodlyFN is this helped!

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Answers

Answer:

0.45/1 = (0.45 × 100)/(1 × 100) = 45/100.

Step-by-step explanation:

How many people surveyed in New York wear Nike's.
In San Francisco 165 people wear Nike's 80 people wear Adidas
In New York 116 people wear Nike's 148 wear Adidas

Answers

Answer:

116

Step-by-step explanation:

it says in the description that 116 people in new york wear nike's

common multiples for 30 21 and 24

Answers

Answer:

The common multiple for 30 21 and 24 is 3

Step-by-step explanation:

30 = 3 × 10

21 = 3 × 7

24 = 3 × 8

Thus, 3 is the common multiple for 30 21 and 24.

-TheUnknownScientist

Pl help it’s for a grade

Answers

Step-by-step explanation:

Given,

1. The given expression is [tex]\sqrt[10]{x^9}[/tex].

We need to write it into exponential form.

We know that,

[tex]\sqrt[a]{x} =x^{1/a}[/tex]

Here, a = 10

So,

[tex]\sqrt[10]{x^9}=(x^9)^{1/10}\\\\=x^{9\times \dfrac{1}{10}}\\\\=x^{9/10}\\\\=x^{0.1}[/tex]

2.

[tex](\sqrt[4]{3y} )^3\\\\=((3y)^3)^{1/4}\\\\=3^{3\times \dfrac{1}{4}}\times y^{3\times \dfrac{1}{4}}\\\\=3^{3/4}y^{3/4}[/tex]

Hence, this is the required solution.

2+2=???
I'm having a lot of trouble solving this complex question and I'm not just giving away points trust me. will give brainiest have a nice day and remember you are valid ​

Answers

Answer:

4

Step-by-step explanation:

rllly

The sum to infinity of a geometric series is 4 and the second term is 1. Find the first,third and fourth terms.

Answers

Answer:

2, 0.5 and 0.25.

Step-by-step explanation:

The nth term an = a1r^(n-1)  where a1 = first term and r = the common ratio.

The sum to infinity = a1/(1-r)  for  -1 < r < 1.

So we have:

Second term a2 = 1 = a1(r)(2-1) = a1r and

4 = a1/(1 - r)

From the first equation:

a1 =1/r

So substituting in the second equation:

4 = 1/ r / (1 - r)

4 = 1 / r - r^2

4r - 4r^2 = 1

4r^2 - 4r + 1 = 0

(2r - 1)(2r - 1) = 0

r = 0.5

So the first term  a1 = 1/ r =1/0.5 = 2.

The third = 1*0.5 = 0.5

and the 4th = 0.5*0.5 = 0.25.

Which of the following equations has the same solution as 3x – 5 = 5x + 11?
A. -5 = 2.2 +11
B. 3.x = 5x + 6
C. 3x + 6 = 5.2
D. 2x – 5 = 11

Answers

Answer: . -5=2x+11

Step-by-step explanation:

Tell whether the events are independent or dependent. Explain PLEASE HELP I WILL GIVE BRAINLIEST!!!

Answers

Answer:

5: independent, 6:independent, 7:independent, 8:dependent, 9:dependent

Step-by-step explanation:

5 is independent because the first roll of the die does nothing to affect the second.

6 is independent because the first flip of the coin does nothing to affect the second

7 is independent because the first draw from the bag does nothing to impact the second, if they didn't place a marble back then it would become dependent.

8 is dependent because by keeping the first marble you change the odds for the second draw. The second draw depends on the first.

9 is dependent because there is a set amount of names placed into this raffle. Say to start you have 12. That means you have a 1/12 chance of being chosen. Once your name is drawn it goes up to a 1/11 chance. The first action directly impacts the second making it dependent.

PLS HELP ON THIS I DONT KNOW

Answers

Answer:

i belive it is the first one.

Step-by-step explanation:

the straight line L passes through the points (0 , 12) and (10 , 4).

Find an equation of the straight line which is parallel to L and passes through the point (5 , -11).

Answers

Answer:

y = - [tex]\frac{4}{5}[/tex] x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 12) and (x₂, y₂ ) = (10, 4)

m = [tex]\frac{4-12}{10-0}[/tex] = [tex]\frac{-8}{10}[/tex] = - [tex]\frac{4}{5}[/tex] ← slope of line L

Parallel lines have equal slopes , then

y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation

To find c substitute (5, - 11) into the partial equation

- 11 = - 4 + c ⇒ c = - 11 + 4 = - 7

y = - [tex]\frac{4}{5}[/tex] x - 7 ← equation of parallel line

The equation of the straight line which is parallel to L and passes through the point (5 , -11) will be;

⇒ y = - 4/5x - 7

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The straight line L passes through the points (0 , 12) and (10 , 4).

And, The equation of the straight line which is parallel to L and passes through the point (5 , -11).

Now,

Since, The straight line L passes through the points (0 , 12) and (10 , 4).

So, Equation of line L is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - 12 = (4 - 12) / (10 - 0)  (x - 0)

⇒ y - 12 = - 8 / 10x

⇒ 10 (y - 12) = - 8x

⇒ 10y - 120 = - 8x

⇒ 10y = - 8x + 120

⇒ y = - 8/10x + 12

⇒ y = - 4/5x + 12

And, The equation of the straight line which is parallel to L and passes through the point (5 , -11).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

y = -4/5x + 12

m = dy/dx = - 4/5

m = - 4/5

Thus, The equation of line with slope 1- 4/5 is,

⇒ y - (-11) = - 4/5 (x - 5)

⇒ y + 11 = - 4/5 (x - 5)

⇒ 5 (y + 11) = - 4x + 20

⇒ 5y + 55 = - 4x + 20

⇒ 5y = - 4x + 20 - 55

⇒ 5y = - 4x - 35

⇒ y = - 4/5x - 7

Thus, The equation of the straight line which is parallel to L and passes through the point (5 , -11) will be;

⇒ y = - 4/5x - 7

Learn more about the equation of line visit:

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