Angle Of Elevation Quiz: Angle Of Elevation Application

1) Find the height of a balloon seen at 30° angle of elevation from 200 m away.

115.5 m

100 m

110 m

105 m

tan(30°) = 0.5774 → height = 200 × 0.5774 = 115.48 ≈ 115.5 m.

Explanation

tan(30°) = 0.5774 → height = 200 × 0.5774 = 115.48 ≈ 115.5 m.

2) Select all statements that are true about tangent and angle of elevation.

Tangent relates height and distance

It is used to find vertical heights

It applies only in right triangles

Tan(θ) = distance/height

Tan(θ) = opposite/adjacent

Tangent compares opposite (height) to adjacent (distance) and works in right triangles.

Explanation

Tangent compares opposite (height) to adjacent (distance) and works in right triangles.

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3) A tree casts a 20 m shadow with the sun’s angle of elevation at 40°. Find the height.

16.8 m

17 m

15 m

14 m

tan(40°) = 0.8391 → height = 20 × 0.8391 = 16.78 ≈ 16.8 m.

Explanation

tan(40°) = 0.8391 → height = 20 × 0.8391 = 16.78 ≈ 16.8 m.

4) A tower is viewed at a 10° angle of elevation from a point 100 m away. Find the tower’s height.

17.6 m

18 m

20 m

15 m

tan(10°) = 0.1763 → height = 100 × 0.1763 = 17.63 ≈ 17.6 m.

Explanation

tan(10°) = 0.1763 → height = 100 × 0.1763 = 17.63 ≈ 17.6 m.

5) A building is 50 m away. The angle of elevation to the top is 30°. Find the height.

28.9 m

25 m

26.5 m

30 m

tan(30°) = 0.5774 → height = 50 × 0.5774 = 28.87 ≈ 28.9 m.

Explanation

tan(30°) = 0.5774 → height = 50 × 0.5774 = 28.87 ≈ 28.9 m.

6) An observer is 40 m away from a tree. The angle of elevation is 45°. Find the height of the tree.

30 m

35 m

40 m

45 m

tan(45°) = 1 → height = 40 × 1 = 40 m.

Explanation

tan(45°) = 1 → height = 40 × 1 = 40 m.

7) Tan(θ) = height/distance when finding height using the angle of elevation.

True

False

True. By definition, tan(θ) = opposite/adjacent, where opposite is the height and adjacent is the horizontal distance.

Explanation

True. By definition, tan(θ) = opposite/adjacent, where opposite is the height and adjacent is the horizontal distance.

8) The formula for finding the height using angle of elevation is height = distance × ______.

Rearranging tan(θ) = height/distance gives height = distance × tan(θ).

Explanation

Rearranging tan(θ) = height/distance gives height = distance × tan(θ).

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9) The angle of elevation to the top of a tower 60 m away is 60°. Find the height.

103.9 m

80 m

100 m

90 m

tan(60°) = 1.732 → height = 60 × 1.732 = 103.92 ≈ 103.9 m.

Explanation

tan(60°) = 1.732 → height = 60 × 1.732 = 103.92 ≈ 103.9 m.

10) If the distance from a tree is 25 m and the angle of elevation is 37°, find the height.

15 m

18.9 m

19 m

20 m

tan(37°) = 0.7536 → height = 25 × 0.7536 = 18.84 ≈ 18.9 m.

Explanation

tan(37°) = 0.7536 → height = 25 × 0.7536 = 18.84 ≈ 18.9 m.

11) A larger angle of elevation means a taller object when the distance is constant.

True

False

True. As angle increases, tan(θ) increases, so the height also increases.

Explanation

True. As angle increases, tan(θ) increases, so the height also increases.

12) A person is 100 m away from a cliff. The angle of elevation is 25°. Find the height.

45 m

47 m

49 m

50 m

tan(25°) = 0.4663 → height = 100 × 0.4663 = 46.63 ≈ 47 m.

Explanation

tan(25°) = 0.4663 → height = 100 × 0.4663 = 46.63 ≈ 47 m.

13) Find the height if distance = 70 m and angle of elevation = 45°.

70 m

65 m

75 m

80 m

tan(45°) = 1 → height = 70 × 1 = 70 m.

Explanation

tan(45°) = 1 → height = 70 × 1 = 70 m.

14) Select all correct formulas for height using tangent.

Height = distance × tan(θ)

Tan(θ) = height/distance

Distance = height/tan(θ)

Tan(θ) = distance/height

Cos(θ) = height/distance

tan(θ) = height/distance can be rearranged as height = distance × tan(θ) or distance = height/tan(θ).

Explanation

tan(θ) = height/distance can be rearranged as height = distance × tan(θ) or distance = height/tan(θ).

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15) The angle of elevation to a hilltop is 20°, and the observer is 100 m away. Find the height.

35 m

36.4 m

40 m

45 m

tan(20°) = 0.3640 → height = 100 × 0.3640 = 36.4 m.

Explanation

tan(20°) = 0.3640 → height = 100 × 0.3640 = 36.4 m.

16) If distance doubles and the angle remains the same, the height also doubles.

True

False

True. height = distance × tan(θ). Doubling distance doubles the height when angle is constant.

Explanation

True. height = distance × tan(θ). Doubling distance doubles the height when angle is constant.

17) In a right triangle, the tangent of an angle equals the ratio of the ______ to the adjacent side.

By definition, tan(θ) = opposite/adjacent, where the opposite side is the height.

Explanation

By definition, tan(θ) = opposite/adjacent, where the opposite side is the height.

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18) If a person is 30 m away from a flagpole and the angle of elevation is 75°, find the height.

110 m

112.1 m

112.2 m

112.3 m

tan(75°) = 3.732 → height = 30 × 3.732 = 111.96 ≈ 112.1 m.

Explanation

tan(75°) = 3.732 → height = 30 × 3.732 = 111.96 ≈ 112.1 m.

19) An observer is 15 m away from a building. The angle of elevation is 60°. Find the height.

25.9 m

26 m

24 m

20 m

tan(60°) = 1.732 → height = 15 × 1.732 = 25.98 ≈ 25.9 m.

Explanation

tan(60°) = 1.732 → height = 15 × 1.732 = 25.98 ≈ 25.9 m.

20) Tan(θ) is always less than 1 for acute angles smaller than 45°.

True

False

True. tan(θ)

Explanation

True. tan(θ)

Angle of Elevation Quiz: Angle of Elevation Application

1) Find the height of a balloon seen at 30° angle of elevation from 200 m away.

2)

What first name or nickname would you like us to use?

2) Select all statements that are true about tangent and angle of elevation.

3) A tree casts a 20 m shadow with the sun’s angle of elevation at 40°. Find the height.

4) A tower is viewed at a 10° angle of elevation from a point 100 m away. Find the tower’s height.

5) A building is 50 m away. The angle of elevation to the top is 30°. Find the height.

6) An observer is 40 m away from a tree. The angle of elevation is 45°. Find the height of the tree.

7) Tan(θ) = height/distance when finding height using the angle of elevation.

8) The formula for finding the height using angle of elevation is height = distance × ______.

9) The angle of elevation to the top of a tower 60 m away is 60°. Find the height.

10) If the distance from a tree is 25 m and the angle of elevation is 37°, find the height.

11) A larger angle of elevation means a taller object when the distance is constant.

12) A person is 100 m away from a cliff. The angle of elevation is 25°. Find the height.

13) Find the height if distance = 70 m and angle of elevation = 45°.

14) Select all correct formulas for height using tangent.

15) The angle of elevation to a hilltop is 20°, and the observer is 100 m away. Find the height.

16) If distance doubles and the angle remains the same, the height also doubles.

17) In a right triangle, the tangent of an angle equals the ratio of the ______ to the adjacent side.

18) If a person is 30 m away from a flagpole and the angle of elevation is 75°, find the height.

19) An observer is 15 m away from a building. The angle of elevation is 60°. Find the height.

20) Tan(θ) is always less than 1 for acute angles smaller than 45°.