This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Trigonometry Application – Height and Distance”.

1. The distance between two objects can be known using trigonometric ratios.

a) True

b) False

View Answer

Explanation: Finding the distance between two objects is one of the different applications of trigonometry. Trigonometry is also used to find the height or length of an object too.

2. One of the applications of trigonometry is used for astronomers to find the distance between two planets.

a) False

b) True

View Answer

Explanation: The length or height or distance between two objects can be known using trigonometry. Trigonometry is applied in astronomy, navigation, architecture, etc.

3. _____ is drawn from the eye of an observer to the targeted object.

a) A parallel line

b) Line of sight

c) Elevation line

d) Depression line

View Answer

Explanation: The line of sight is a line that is drawn from the eye of an observer to the targeted object viewed by the observer and the line of sight is required to form the angle of elevation.

4. What happens to the angle of elevation if the height of a tower, the distance between the tower and the observer is doubled?

a) Doubled

b) halved

c) Tripled

d) Remains the same

View Answer

Explanation: The angle of elevation is independent of the height of an object and the distance between the object and the observer. So, the angle of elevation remains the same when the height of a tower, the distance between the tower and the observer is doubled.

5. The angle of depression is always a/an _____ angle.

a) right

b) obtuse

c) complete

d) acute

View Answer

Explanation: The angle of elevation is an acute angle. The angles that are less than 90° are called as acute angles. The angle of depression is also an acute angle.

6. A pole stands vertically on the floor. From a point, it is 120 meters away from the foot of the pole and the angle of elevation is 45° then find the height of the pole.

a) 100 meters

b) 180 meters

c) 120 meters

d) 10 meters

View Answer

Explanation: In the figure, BC is the height of the pole.

In ∆ABC, Tan 45° = \(\frac {BC}{AB}\)

1 = \(\frac {BC}{AB}\)

1 = \(\frac {BC}{120}\)

BC = 120 meters

7. A slope is built against a wall which makes an angle 30° with the ground and the height of the wall is 2 meters. Find the length of the slope in meters.

a) 2

b) 4

c) 1

d) 3

View Answer

Explanation: AC is the length of the slope in ∆ABC.

sin 30° = \(\frac {AB}{AC}\)

\( \frac {1}{2} = \frac {2}{AC}\)

AC = 4 meters

8. A slide should be built in a park that has to be set up at 10 meters height and also 10 meters away from the support. What should be the angle of elevation?

a) 45°

b) 30°

c) 60°

d) 90°

View Answer

Explanation: The angle between AC and BC is the angle of elevation that has to be found.

tan θ = \(\frac {AB}{BC} = \frac {10}{10} \)

Tan θ = 1

θ = 45°

9. A tree trunk of height 12 meters is erected with the support of three metal chains. An angle of 60° is made by each metal chain with the tree trunk. Find the length of the metal chain.

a) 32 meters

b) 10meters

c) 24 meters

d) 18 meters

View Answer

Explanation: We have to find the length of the metal chain AC.

cos 60° = \(\frac {BC}{AC}\)

\( \frac {1}{2} = \frac {12}{AC}\)

AC = 24 meters

10. A ship has to cross a sea by making an angle of 30° and with a distance of 200 meters to reach the shore then find the width of the sea.

a) 300 meters

b) 100 meters

c) 110 meters

d) 50 meters

View Answer

Explanation: The width of the river is BC in the figure.

sin 30° = \(\frac {BC}{AC}\)

\( \frac {1}{2} = \frac {BC}{200}\)

BC = 100 meters

**Sanfoundry Global Education & Learning Series – Mathematics – Class 10**.

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