This set of Aptitude Questions and Answers (MCQs) focuses on “Angle of Depression”.

1. In which of the following cases angle of depression is formed?

a) Looking up

b) Looking out

c) Looking down

d) Line of sight

View Answer

Explanation: Looking down is the correct option as angle of depression is formed in the case of looking down.

2. A person is standing at the top of a tower and looking down at an angle of depression of 60 degree at a distance of 30 m. What will be the height of this tower?

a) 30√3 m

b) 60 / √3 m

c) 60√3 m

d) 30 / √3 m

View Answer

Explanation: Given,

Angle of depression = 60, base distance = 30 m.

Let the height of the tower = h m.

➩ tan 60 = h / b

➩ √3 = h / 30

➩ h = 30√3 m

3. A light house is 65 m tall. The angle of depression from the top is 45 degrees at distance x m. What will be the value of x?

a) 65 / √3 m

b) 65 m

c) 65√3 m

d) 130 / √3 m

View Answer

Explanation: Given,

Angle of depression = 45 – degree, height = 65 m, base distance = x m.

➩ tan 45 = h / b

➩ 1 = 65 / b

➩ b = 65 m

4. If the height of a tower and the distance of the point of observation are both doubled, then what will happen to the angle of depression?

a) Same

b) Increases

c) Decreases

d) No relation

View Answer

Explanation: Same is the correct option is if the height of a tower and the distance of the point of observation are both increased or decreased in the same ratio then the angle of depression will always remain same.

5. If the height of a pole and the length of its shadow are equal, then what will be the value of its angle of depression?

a) 30 degree

b) 37 degree

c) 45 degree

d) 53 degree

View Answer

Explanation: Given,

Height of tower = length of shadow

➩ tan A = height of tower / length of shadow

➩ tan A = 1

➩ A = 45 degree

6. An object is placed 20 m away from the wall of a pool. The angle of depression of the object from the pool platform is 53 degree, then what will be the diagonal distance he will have to swim to get the object?

a) 200 / √3 m

b) 50√3 m

c) 100 / 3√3 m

d) 100 / 3 m

View Answer

Explanation: Given,

Angle = 53 degree, base = 20 m.

Let the diagonal distance = d m.

➩ Cos 53 = base / diagonal

➩ 3 / 5 = 20 / d

➩ d = 100 / 3 m

7. A skier took 60 s to travel down a snowy slope of vertical height 400 m. If the angle of depression is 60 degree, then what will be the speed of the skier in m / s?

a) 7.84

b) 8.42

c) 6.89

d) 6.24

View Answer

Explanation: Given,

Angle = 60 – degree, perpendicular height = 400 m, time taken = 60 s.

Let the distance traversed = x m.

➩ sin 60 = perpendicular / hypotenuse

➩ √3 / 2 = 400 / x

➩ x = 800 / √3 m

Speed = distance / time = (800 / √3) / 60 = 7.84 m / s

8. Which of the following options are correct?

a) Angle of elevation and angle of depression are always equal

b) Angle of elevation and angle of depression are never equal

c) Angle of elevation and angle of depression may or may not be equal

d) Angle of elevation and angle of depression are both obtuse angles

View Answer

Explanation: “Angle of elevation and angle of depression may or may not be equal” is the correct option as that angle of elevation and angle of depression may or may not be equal. When the roof and floor are parallel, they are equal else they are not.

9. An airplane is flying at the height of 20 km above the ground. From there it makes an angle of depression of 37 degree to the landing spot. What will be the horizontal and diagonal distance (in km) between the plane and the landing spot?

a) 80 / 3, 100 / 3

b) 100 / 3, 80 / 3

c) 100√3, 80 / √3

d) 80√3, 100 / √3

View Answer

Explanation: Given,

Angle = 37 – degree, vertical height = 20 km.

Let the horizontal height = b, diagonal height = h.

➩ sin 37 = vertical height / diagonal height

➩ 3 / 5 = 20 / h

➩ h = 100 / 3

Thus, h = 100 / 3 km.

➩ tan 37 = vertical height / horizontal height

➩ 3 / 4 = 20 / b

➩ b = 80 / 3 km

10. What will be the value of angle of depression when the object and the observer lie in the same line?

a) 0

b) 30

c) 45

d) 90

View Answer

Explanation: When the object and the observer lie in the same line the angle of depression in such cases is zero.

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