In Δ​NMP, m∠MNP =45°​, MN =7.5 feet, and MP=5 feet. How many triangles can be drawn when given this​ information?

Answer:1,706

Step-by-step explanation:

Add

Answer:

58,050,000 grams= 58050kg

Step-by-step explanation:

58059kg is the answer

Answer:

Solution to Problem 1:

Use the fact that the sum of all three angles of a triangle is equal to 180 o to write an equation in C.

A + B + C = 180 o

Solve for C.

C = 180 o - (A + B) = 43 o

Use sine law to write an equation in b.

a / sin(A) = b / sin(B)

Solve for b.

b = a sin (B) / sin(A) = (approximately) 5.4 cm

Use the sine law to write an equation in c.

a / sin(A) = c / sin(C)

Solve for c.

c = a sin (C) / sin(A) = (approximately) 7.1 cm

Problem 2

The angle of elevation to the top C of a building from two points A and B on level ground are 50 degrees and 60 degrees respectively. The distance between points A and B is 30 meters. Points A, B and C are in the same vertical plane. Find the height h of the building(round your answer to the nearest unit).

diagram problem 2

Solution to Problem 2:

We consider triangle ABC. Angle B internal to triangle ABC is equal to

B = 180 o - 60 o = 120 o

In the same triangle, angle C is given by.

C = 180 o - (50 o + 120 o) = 10 o

Use sine law to find d.

d / sin(50) = 30 / sin(10)

Solve for d.

d = 30 *sin(50) / sin(10)

We now consider the right triangle.

sin (60) = h / d

Solve for h.

h = d * sin(60)

Substitute d by the expression found above.

h = 30 *sin(50) * sin(60) / sin(10)

Use calculator to approximate h.

h = (approximately) 115 meters.

Problem 3

A triangle ABC has side a = 12 cm, side b = 19 cm and angle A = 80 o (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).

Solution to Problem 3:

Use sine law to write an equation in sin(B).

a / sin(A) = b / sin(B)

Solve for sin(B).

sin (B) = (b / a) sin(A) = (19/12) sin(80) = (approximately) 1.6

No real angle B satisfies the equation

sin (B) = 1.6

The given problem has no solution.

Problem 4

A triangle ABC has side a = 14 cm, side b = 19 cm and angle A = 32 o (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).

Solution to Problem 4

Use sine law to write an equation in sin(B).

a / sin(A) = b / sin(B)

Solve for sin(B).

sin (B) = (b / a) sin(A) = (19/14) sin(32) = (approximately) 0.7192

Two angles satisfy the equation sin (B) = 0.7192 and the given problem has two solutions

B1 = 46.0 o and B2 = 134 o

Solution 1: Find angle C1 corresponding to B1

C1 = 180 - B1 - A = 102 o

Solution 1: Find side c1 corresponding to C1

c1 / sin(C1) = a / sin(A)

c1 = 14 sin(102) / sin(32) = (approximately) 25.8 cm

Solution 2: Find angle C2 corresponding to B2

C2 = 180 - B2 - A = 14 o

Solution 2: Find side c2 corresponding to C2

c2 / sin(C2) = a / sin(A)

c1 = 14 sin(14) / sin(32) = (approximately) 6.4 cm

Exercises

1. A triangle ABC has angle A = 104 o, angle C = 33 o and side c = 9 m. Solve the triangle ABC by finding angle B and sides a and b.(round answers to 1 decimal place).

2. Redo problem 2 with the distance between points A and B equal to 50 meters.

Solutions to Above Exercises

1. B = 43 o, a = 16.0 m , b = 11.3 m

2. 191 meters.

More References and Links to Sine and Cosine Laws

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Triangles

Triangle Problems

Answer:

r = 16 units

Step-by-step explanation:

From the figure attached,

AB is the tangent drawn from a point A to the circle C.

BC = r [Radius of the circle]

Length of AC = (18 + r)

AB = 30

By the property of a tangent drawn to a circle,

"Radius of a circle and tangent are perpendicular to each other"

AB ⊥ BC

By applying Pythagoras theorem in ΔABC,

AB² + BC² = AC²

(30)² + r² = (r + 18)²

900 + r² = r² + 36r + 324

36r = 900 - 324

r = [tex]\frac{576}{36}[/tex]

r = 16 units

Answer:

31

Step-by-step explanation:

They're technically asking you to find the missing angle. 61+57 is 118. 180-118 is 62. Since they're asking  2x, you do 62 divided by 2, which is 31.

Answer:

x= 40°

Step-by-step explanation:

since the angles of the quadrilateral add up to 360°

then to find the agle x:

step:1

add alll the angles given in the quadrilateral

100+120+100

= 320

step:2

now subtract the sum of the quadrilateral from the sum of alll angles

360°-320° = 40°

therefore the answer equates to 40°

Answer:

360-(100+120+100)

360-320

40

Answer:

arc EI = 103°

arc EGI = 257°

Step-by-step explanation:

arc HI = 77° because they are alternate angles

arc EI = (360° - 77° - 77°)/2 = 103°

arc EGI = 360° - 103° = 257°

Answer:

Step-by-step explanation:

Dimensions:

Area is:

Answer:

the rule to remember is that opposites attract. every magnet has both a north and a South pole. when you place the North Pole of one magnet near the South Pole of another magnet, they are attracted to one another.

Step-by-step explanation:

Hope this helped Mark BRAINLIEST!!

Answer:

The magnets have different poles facing each other ( N/S > < S/N )

Answer:

82 degrees

Step-by-step explanation:

It should all equal 180 so 52+46=98 and 180-98 is 82

Answer: the answer is 20.

Answer:

rose: $2.75; carnation: $1.25

Step-by-step explanation:

-10 and -1

Step-by-step explanation:

Answer:

-10, and -1

Step-by-step explanation:

Answer:

Answer is 980.

Step-by-step explanation:

First what you should do it figure out 14^2 which is 196 then you times that by 5 which gets you 980. Hope this helps.

Answer:

The answer is 980.

Step-by-step explanation: to follow pemdas you first start with the exponents for there are no parenthesis. So to do this 14^2 is just 14x14 with is 196. Then you take that and multiply it by the 5 to get your end product. 196x5=980.

Hope this helps.

Answer:

1

Step-by-step explanation:

Hope This helps! : )

Answer:

the answer i got is 10

im taking the same test right now

Step-by-step explanation:

Answer:

1. their

2. your

3. there

4. You're

5. they're

6. it's

Step-by-step explanation:

Answer: Below

1. Their

2. i dont know sorry

3. There

4. Your're ( I think, I am not good at the Ys

5. They're

6. I think it's

Please do not take these answer for granted I am trying my best

Thank you and have a great nae nae

Answer:

0%

Step-by-step explanation:

Since there are no red marbles in the bag, there is no chance that a red marble will be picked.

Answer:

10, 12, 30 - no

6, 8, 10 - yes

8, 16, 24 - no

20, 21, 28 - no

Step-by-step explanation:

Just plug them into the Pythagorean Theorem equation (a² + b² = c²)

Brₐinliest plz close to leveling up

Answer:

1.

Blank 1: y

Blank 2: x

2.

Blank 1: x

Blank 2: y

Step-by-step explanation:

The reflection of a point along y-axis means the y value stays the same and the x-value changes its sign.

Blank 1: y

Blank 2: x

The reflection of a point along x-axis means the x value stays the same and the y-value changes its sign.

Blank 1: x

Blank 2: y

Answer:

B) <

Step-by-step explanation:

b is the answer because -1 is bigger than 0 so, the answer is b.

Answer:

n<

9/8

explanation

simplify n+ -7/4 < -5/8

add 7/4 to both sides

= n< 9/8

Hi there!

To begin, we can distribute sec²x with (1 - sin²x):

= sec²x - sec²xsin²x

Which simplifies to:

= sec²x - tan²x

Recall the Pythagorean identity:

1 + tan²x = sec²x

Rearrange alike to the solved for expression above:

1 = sec²x  - tan²x

Thus, using the Pythagorean Identity, sec²x(1 - sin²x) = 1.

Answer:

The answer is 22.

Explanation:

Multiply -1 by -9.

[tex]13 + 9[/tex]

Add 13 + 9.

[tex]22[/tex]

Therefor, the answer is 22.

Answer:

b. The quadratic is expressed in standard form; a=8, b= -5, and c=3.

Answer:

340; 15

Step-by-step explanation:

221 is 65% of 221

11.25 is 75% of 15

Answer:

75 units

Step-by-step explanation:

Answer:

5 units

Step-by-step explanation:

answer given by IXL

Answer:

3 inches per hour

Step-by-step explanation:

hope this helps

Answer:

160 for the rectangle table and 91 for the round table