This set of Aptitude Questions and Answers (MCQs) focuses on “Angle of Depression – Set 2”.
1. Which of the following options is wrong about angle of depression?
a) It can be an acute angle
b) It can be equal to the angle of elevation
c) It can be an obtuse angle
d) It is formed when someone looks down at something
View Answer
Explanation: Obtuse angle is the correct answer as it is a false statement about angle of depression. Angle of depression can never be an obtuse angle.
2. A bird flying at a height of 2000 m from the ground. It spots a worm at an angle of depression of 30 degree. What is the base distance (in m) of the worm?
a) 2000 / √3
b) 2000√3
c) 1000√3
d) 1000 / √3
View Answer
Explanation: Given,
Angle = 30 – degree, height = 2000 m
Let the base distance = b m.
➩ tan 30 = height / base distance
➩ 1 / √3 = 2000 / b
➩ b = 2000√3 m
3. A kite is flying at a vertical height of 500 m making an angle of depression of 45 degree. What will be the length of thread required in this case?
a) 500√3 m
b) 500√2 m
c) 500 / √2 m
d) 500 m
View Answer
Explanation: Given,
Angle = 45 – degree, height = 500 m
Let the length of thread (diagonal) = d m.
➩ sin 45 = height / diagonal
➩ 1 / √2 = 500 / d
➩ d = 500√2 m
4. An airplane is flying at a certain height. It makes an angle of depression of 45 degree to the landing spot with horizontal distance between the two being 1100 m. What is the vertical height at which the plane is flying?
a) 1100 m
b) 1100√2 m
c) 1100 / √3 m
d) 1100√3 m
View Answer
Explanation: Given,
Angle = 45, Horizontal distance = 1100m
Let the vertical heigh = h.
➩ tan 45 = vertical height / horizontal distance
➩ 1 = h / 1100
➩ h = 1100 m
5. Which of the following options correctly defines the angle from the horizontal downward to an object?
a) Angle of inclination
b) Line of sight
c) Angle of depression
d) Angle of elevation
View Answer
Explanation: Angle of depression is correct as the angle from the horizontal downward to an object is known as the angle of depression.
6. A bus took 40 seconds to drive down a slopy hill of height 800 m. If the angle of depression of the path is 30 degree, then what was the speed of the bus?
a) 1600 / √3 m
b) 800√2 m
c) 800 m
d) 1600 m
View Answer
Explanation: Given,
Angle = 30 – degree, time = 40 seconds, height = 800 m
Let the length of the path = h m.
➩ sin 30 = height / length of path
➩ \(\frac {1}{2}\) = 800 / h
➩ h = 1600 m
7. Which of the following options is correct when angle of elevation and angle of depression are measured between two parallel planes?
a) Angle of elevation = angle of depression
b) Angle of elevation < angle of depression
c) Angle of elevation > angle of depression
d) Angle of elevation and angle of depression have no relation
View Answer
Explanation: Angle of elevation is equal to angle of depression is correct as when angle of elevation and angle of depression are measured between two parallel planes, they become equal.
8. A person is standing at the top of a tower and looking down at an angle of depression of 37 degree at a distance of 50 m. What will be the height of this tower?
a) 56 m
b) 75 m
c) 37.5 m
d) 47 m
View Answer
Explanation: Given,
Angle = 37, base distance = 50 m
Let the height of the tower = h m.
➩ tan 37 = height / base distance
➩ \(\frac {3}{4}\) = h / 50
➩ h = 3 * 50 / 4
➩ h = 75 / 2 m = 37.5 m
9. Which of the following values of angle of depression is not possible?
a) 91 degree
b) 78 degree
c) 83 degree
d) 56 degree
View Answer
Explanation: Angle of depression can never be greater than 90 degree. Thus, 91 degree is not possible.
10. A ball rolls down a slope having vertical height and base distance equal to 40 m. What will be the length of the slope?
a) 40 / √2 m
b) 20√2 m
c) 20 / √2 m
d) 40√2 m
View Answer
Explanation: Given,
Vertical height = 40 m, base distance = 40 m
Let the angle = A, slope length = h m.
➩ tan A = vertical height / base distance
➩ tan A = 40 / 40
➩ A = 45
Now,
➩ Sin 45 = vertical height / slope length
➩ 1 / √2 = 40 / h
➩ h = 40√2 m
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