Q: A hot air balloon is rising vertically. Your friend is standing on level ground, 100 feet away from your point of lift-off, and measures the angle of elevation to the balloon as $$37.2^\circ. $$What is the height of the balloon above the ground? (Round your answer to the nearest foot.)

$$h = 100 \cdot \tan(37.2^\circ) \approx 76 ft$$

Q: Given a right triangle where the adjacent side to angle $$\theta is 100 ft $$and the opposite side is $$h$$, which trigonometric function relates $$h$$ and $$\theta$$?

$$\tan(\theta) = \frac{h}{100}$$

Q: A bearing is measured as the angle from the north-south line to the line joining two points. If the bearing from the origin to point $$P is$$ $$\theta$$, which of the following best describes $$\theta$$?

$$\theta is $$the angle measured clockwise from the north direction.

Q: Suppose you are 100 ft away from a balloon and the angle of elevation is $$45^\circ. $$What is the height of the balloon?

$$h = 100 \cdot \tan(45^\circ) = 100 ft$$

Q: If the angle of elevation to a balloon is $$60^\circ$$ and you are 100 ft from the point directly below the balloon, what is the height of the balloon?

$$h = 100 \cdot \tan(60^\circ) \approx 173 ft$$

Q: A pilot measures the angle of elevation to a weather balloon as $$30^\circ$$ from a point 200 ft away. What is the height of the balloon?

$$h = 200 \cdot \tan(30^\circ) \approx 115.5 ft$$

Q: Which of the following best describes the process for finding the height of an object using the angle of elevation and horizontal distance?

Use $$h = d \cdot \tan(\theta)$$, where $$d is $$the horizontal distance and $$\theta is $$the angle of elevation.

Q: If you are standing 150 ft from a building and the angle of elevation to the top is $$25^\circ$$, what is the height of the building?

$$h = 150 \cdot \tan(25^\circ) \approx 70 ft$$

Q: A surveyor is 120 ft from a tower and measures the angle of elevation to the top as $$40^\circ. $$What is the height of the tower?

$$h = 120 \cdot \tan(40^\circ) \approx 101 ft$$

Q: Which of the following is NOT a correct step in solving for the height of an object using the angle of elevation?

Using $$\cos(\theta) = \frac{h}{d} to $$solve for $$h.$$

Question 1

A hot air balloon is rising vertically. Your friend is standing on level ground, 100 feet away from your point of lift-off, and measures the angle of elevation to the balloon as $$37.2^\circ. $$What is the height of the balloon above the ground? (Round your answer to the nearest foot.)

Accepted Answer

$$h = 100 \cdot 	an(37.2^\circ) \approx 76 ft$$

Question 2

Given a right triangle where the adjacent side to angle $$	heta is 100 ft $$and the opposite side is $$h$$, which trigonometric function relates $$h$$ and $$	heta$$?

Accepted Answer

$$	an(	heta) = \frac{h}{100}$$

Question 3

If the angle of elevation to a balloon increases, but the horizontal distance remains the same, what happens to the height of the balloon?

Accepted Answer

The height increases.

Question 4

A bearing is measured as the angle from the north-south line to the line joining two points. If the bearing from the origin to point $$P is$$ $$	heta$$, which of the following best describes $$	heta$$?

Accepted Answer

$$	heta is $$the angle measured clockwise from the north direction.

Question 5

Suppose you are 100 ft away from a balloon and the angle of elevation is $$45^\circ. $$What is the height of the balloon?

Accepted Answer

$$h = 100 \cdot 	an(45^\circ) = 100 ft$$

Question 6

If the angle of elevation to a balloon is $$60^\circ$$ and you are 100 ft from the point directly below the balloon, what is the height of the balloon?

Accepted Answer

$$h = 100 \cdot 	an(60^\circ) \approx 173 ft$$

Question 7

A pilot measures the angle of elevation to a weather balloon as $$30^\circ$$ from a point 200 ft away. What is the height of the balloon?

Accepted Answer

$$h = 200 \cdot 	an(30^\circ) \approx 115.5 ft$$

Question 8

Which of the following best describes the process for finding the height of an object using the angle of elevation and horizontal distance?

Accepted Answer

Use $$h = d \cdot 	an(	heta)$$, where $$d is $$the horizontal distance and $$	heta is $$the angle of elevation.

Question 9

If you are standing 150 ft from a building and the angle of elevation to the top is $$25^\circ$$, what is the height of the building?

Accepted Answer

$$h = 150 \cdot 	an(25^\circ) \approx 70 ft$$

Question 10

A surveyor is 120 ft from a tower and measures the angle of elevation to the top as $$40^\circ. $$What is the height of the tower?

Accepted Answer

$$h = 120 \cdot 	an(40^\circ) \approx 101 ft$$

Question 11

Which of the following is NOT a correct step in solving for the height of an object using the angle of elevation?

Accepted Answer

Using $$\cos(	heta) = \frac{h}{d} to $$solve for $$h.$$

Question 12

If the bearing from the origin to a point $$P is$$ $$60^\circ$$, which direction is $$P$$ located relative to the origin?

Accepted Answer

Northeast

Question 13

A drone is flying such that the angle of elevation from a point 80 ft away is $$70^\circ. $$What is the height of the drone?

Accepted Answer

$$h = 80 \cdot 	an(70^\circ) \approx 220 ft$$

Question 14

If you are 50 ft from a tree and the angle of elevation to the top is $$80^\circ$$, what is the height of the tree?

Accepted Answer

$$h = 50 \cdot 	an(80^\circ) \approx 284 ft$$

Solving Right Triangle Problems Using Trigonometry (Hot Air Balloon Example)

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