Triangle lurlurl, u, r has a uniform thickness of 2.52.52, point, 5, as shown at left. the length of \overline{ud} ​ud ​ ​​ start overline, u, d, end overline, which is the height of the triangle, is 25\sqrt325√ ​3 ​ ​​ 25, square root of, 3, end square root. the triangle has a right angle at vertex uuu and an angle of \dfrac\pi6 ​6 ​ ​π ​​ start fraction, pi, divided by, 6, end fraction at vertex rrr. given that the width, www, of the shaded triangle is about 50\sqrt{3}50√ ​3 ​ ​​ 50, square root of, 3, end square root, what is the height, hhh, of the shaded triangle to the nearest tenth?

Answer:

37.5

Step-by-step explanation:

The line which marks the height 25\sqrt325  

3

​  

25, square root of, 3, end square root of the large triangle is vertical, and the base of the triangle is horizontal, so their intersection is a right angle. The angles in the large triangle add up to \piπpi, so the remaining angle is:

\qquad \begin{aligned} \pi - \dfrac\pi2 - \dfrac\pi6 =& \dfrac\pi3 \end{aligned}  

π−  

2

π

​  

−  

6

π

​  

=

​  

3

π

​  

​  

The original triangle L U R is shown, but now the length of segment U D is shown to be '25 times the square root of 3', and angle U L R is shown to have a measure of ' pi divided by 3' radians.

The original triangle L U R is shown, but now the length of segment U D is shown to be '25 times the square root of 3', and angle U L R is shown to have a measure of ' pi divided by 3' radians.

Hint #2

Looking at the left triangle ULDULDU, L, D, the hypotenuse length LULUL, U is:

\qquad \begin{aligned} \dfrac{25\sqrt3}{\sin\!\left({\Large\frac\pi3}\right)} \end{aligned}  

sin(  

3

π

​  

)

25  

3

​  

​  

​  

Looking at the big triangle LURLURL, U, R, we see that the base length LRLRL, R is:

\qquad \begin{aligned} &\left(LU\right)\dfrac{1}{\sin\!\left({\Large\frac\pi6}\right)} \\ \\ =&\left(\dfrac{25\sqrt3}{\sin\!\left({\Large\frac\pi3}\right)}\right)\dfrac{1}{\sin\!\left({\Large\frac\pi6}\right)} \\ \\ =&\left(\dfrac{25\sqrt3}{ \quad\large\frac{\sqrt{3}}{2}\quad }\right)\dfrac{1}{ \quad\large\frac{1}{2}\quad } \\ \\ =&\left(\dfrac{25}{ \quad\large\frac{1}{2}\quad }\right)\dfrac{1}{ \quad\large\frac{1}{2}\quad } \\ \\ =&100 \\ \end{aligned}  

=

=

=

=

​  

(LU)  

sin(  

6

π

​  

)

1

​  

⎝

⎜

⎛

​  

sin(  

3

π

​  

)

25  

3

​  

​  

⎠

⎟

⎞

​  

sin(  

6

π

​  

)

1

​  

⎝

⎜

⎛

​  

2

3

​  

​  

25  

3

​  

​  

⎠

⎟

⎞

​  

2

1

​  

1

​  

(  

2

1

​  

25

​  

)  

2

1

​  

1

​  

100

​  

Hint #3

The large triangle has uniform thickness, so the inner triangle's sides are parallel to the outer triangle's sides. Therefore, the inner triangle's angles are congruent to the outer triangle's angles. The two triangles are similar.

Hint #4

Similar triangles have proportional lengths, so we can set up the equation:

\qquad \begin{aligned} \dfrac{h}{w} =& \dfrac{H}{W} \\ \\ \dfrac{h}{50\sqrt{3}} \approx& \dfrac{25\sqrt3}{100} \end{aligned}  

w

h

​  

=

50  

3

​  

h

​  

≈

​  

W

H

​  

100

25  

3

​  

​  

​  

Hint #5

\qquad\qquad\, \begin{aligned} \dfrac{h}{50\sqrt{3}} \approx& \dfrac{\sqrt3}{4} \\ \\ {h} \approx& \dfrac{{50\sqrt{3}}\sqrt3}{4} \\ \\ {h} \approx& \dfrac{25\cdot3}{2} \\ \\ h \approx& 37.5 \\ \\ \end{aligned}  

50  

3

​  

h

​  

≈

h≈

h≈

h≈

​  

4

3

​  

​  

4

50  

3

​  

3

​  

​  

2

25⋅3

​  

37.5

​  

Hint #6

To the nearest tenth, the height of the inner triangle is:

\qquad\qquad\, \begin{aligned} h \approx& 37.5 \end{aligned}  

h≈

​  

37.5

​  

*note: The answers 37.337.337, point, 3 and 37.437.437, point, 4 may have been obtained by other methods of solving for hhh since this is an approximation. Those answers are also accepted as correct.

Two triangles are similar if the sides of both triangles can be represented as equivalent ratios. The height of the shaded triangle is 37.5 units.

Given that:

[tex]\overline{UD} = 25\sqrt 3[/tex]

[tex]w = 50\sqrt3[/tex]

See attachment

First, we calculate side length [tex]\overline{LD}[/tex].

This calculated using tangent trigonometry ratio

[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]

So, we have:

[tex]\tan(90-\frac{\pi}{3}) = \frac{\overline{UD}}{\overline{LD}}[/tex]

[tex]\tan(90-30) = \frac{\overline{UD}}{\overline{LD}}[/tex]

[tex]\tan(60) = \frac{\overline{UD}}{\overline{LD}}[/tex]

This gives:

[tex]\tan(60^o) = \frac{25\sqrt3}{\overline{LD}}[/tex]

Make LD the subject

[tex]\overline{LD}= \frac{25\sqrt3}{\tan(60^o)}[/tex]

[tex]\overline{LD}= \frac{25\sqrt3}{\sqrt 3}[/tex]

[tex]\overline{LD}= 25[/tex]

Next, we calculate side length [tex]\overline{DR}[/tex].

This calculated using tangent trigonometry ratio

[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]

So, we have:

[tex]\tan(\frac{\pi}{6}) = \frac{\overline{UD}}{\overline{DR}}[/tex]

This gives:

[tex]\tan(30^o) = \frac{25\sqrt3}{\overline{DR}}[/tex]

Make DR the subject

[tex]\overline{DR}= \frac{25\sqrt3}{\tan(30^o)}[/tex]

[tex]\overline{DR}= \frac{25\sqrt3}{1/\sqrt 3}[/tex]

[tex]\overline{DR}= 25\sqrt3 \times \sqrt 3[/tex]

[tex]\overline{DR}= 25 \times 3[/tex]

[tex]\overline{DR}= 75[/tex]

Calculate side length [tex]\overline{LR}[/tex]

[tex]\overline{LR} = \overline{LD}+\overline{DR}[/tex]

[tex]\overline{LR} = 25+75[/tex]

[tex]\overline{LR} = 100[/tex]

Because the triangle has a uniform thickness, the small and the big triangle are similar triangles.

So, the height (h) is calculated using the following equivalent ratios

[tex]h:w =\overline{UD}:\overline{LR}[/tex]

Express as a fraction

[tex]\frac hw =\frac{\overline{UD}}{\overline{LR}}[/tex]

Make h the subject

[tex]h =\frac{\overline{UD}}{\overline{LR}} \times w[/tex]

Substitute known values

[tex]h =\frac{25\sqrt3}{100} \times 50\sqrt 3[/tex]

[tex]h =\frac{3750}{100}[/tex]

[tex]h =37.50[/tex]

Hence, the height of the shaded triangle is 37.5 units.

Read more about similar triangles at:

https://brainly.com/question/16919171

PLZ HELP!!! URGENT!!​

PLEASE HELP I WILL MAKE BRAINLIEST

Janice has 400g of sugar and 2 kg of flour. She says that the ratio of sugar to flour simplifies to 200:1. Explain why she is incorrect and give the correct answer.

3. Write each number as a product of its prime factors:
a) 48
b) 441
c) 420
d) 1617
de 10​

800 time 40 divided by 6 equals

what is the total cost of a $52 lunch with a 20% tip?

I need help in this question

Need help po. Salamat

At the end of summer sale, an air conditioner that sold for $310 was discounted for 21%. What was the sale price?

¿Si tienes un cilindro de 12 m de diámetro y un prisma de base cuadrada de 12m de lado cual tiene mayor volumen si la altura es la misma?

Which equations have no solution?
Select all that apply.
A X + 5 = x - 5
B 0.5y = 0
CX-7 = x - 7
D 9(-1 + x) + 1 = 12x + 1
E 8+ 4. f = 4(3+f)

The table shows the number of passengers that can be transported in a company’s vans. How many passengers can be transported in five vans? Vans Passengers 1 12 2 24 3 36 4 48 5 ? 6 72 passengers

PLEASE HELP>YOU CAN LITERALLY SAVE MY LIFE
What is the total bill you would leave for a $22 haircut and a 15% tip?

and

What is the total bill for a $54 dinner with a 5% sales tax and a 20% tip?

What two numbers go there

Eşit sayıda yolcu taşıyan 3 otobüste toplam 93 yolcu vardır. Otobülerden birer
tane yolcu iniyor otobüste kaç yolcu kalır?​

Identify whether the expression is a polynomial, and if so, determine the correct type.
y-3x+4

You go to the restaurant and order $137.00 worth of food. You decided to tip the waiter 18%. You also have to pay tax of 6.5% on the original bill. What is the final cost of the meal?

k+ 6 ≥ 19, if k = 11

HELP are all three of these are either
One Unique Triangles
Multiple Triangles
No triangles

A student is asked to write a report about the population growth of two countries A and B. The population of these two countries over the past five years is shown in the table below, The population of both countries is expected to continue to grow at the same rate. Which if the following statements can the students use in their report to accurately describe the population of Country A? Select two that apply. it is decreasing each year at a constant rate., It is increasing linearly., It will always be less than the population of Country B., It is increasing exponentially., It will eventually exceed the population of Country B lo

Gerald is conducting an experiment with 3 possible outcomes. Kasey is conducting an experiment with 20 possible
outcomes.

Which statement best relates the possible outcomes to the number of trials needed to produce results
similar to their predicted outcomes?
A) Gerald will need to conduct more trials than Kasey because there are fewer possible outcomes in his experiment.

B)Gerald will need to conduct fewer trials than Kasey because there are fewer possible outcomes in his experiment.

C)Gerald will need to conduct more trials because he needs to make up for the difference in the number of possible
outcomes.

D)Gerald will need to conduct fewer trials because experimental and theoretical results in experiments with small
numbers of possible outcomes are the same.

Which of the following statements are ALWAYS true?


A rhombus is a kite.

A rhombus is a parallelogram.

A rhombus is a square.

A rhombus is a quadrilateral.

Jonathan says he knows that 1/2 of 2 1/2 is 1 1/4 and he knows that 5/8 is almost one half if you use estimation. but he is not sure whether 5/18 x 2 1/2 will be more or less than 1 1/4

I NEED HELP LIKE NOW!!!! PLEASE!

Rewrite y = sqrt16x+80 - 4 to make it easy to graph using a translation. Describe the graph.

Thank you!

I NEED SERIOUS HELP I AM HAVING MATH EXAM SOON

PLEASEEEEEEEEEE HELP ME IM PREPARING WITH THE PPTS MY TEACHERS HAVE GAVE ME BUT THEY GAVE NO ANSWER AND IM NOT ABLE TO SOLVE THIS(I asked this before itself but never got an answer so with extra details I'm hoping I will get some answers) its my 4th time my first try no one answered so I put another one then I forgot to attach the photo and third time a person wasted your chances so this my 4th time BUT PLEASE HELP MEHHH

can someone help me with this problem, please?

which method would i use to solve ax^2+c=d? justify your answer.

Kiran said that this diagram can show the solution to 16÷8=? or 16÷2=?, depending on how we think about the equations and the “?”.

EXPLAIN why he is correct.

ayuda por favor 5.800%(-10)​

Question 9 of 9
Which of the expressions are equivalent to the one below? Check all that
apply.
(4.1)-6
O A. (1 : 4) - 6
B. 4. (1-6)
C. 6-(1.4)
O D. (4+ 1) - 6
SWAMIT