This set of Aptitude Questions and Answers (MCQs) focuses on “Angle of Elevation – Set 2”.
1. An observer 1.5 m tall is 23.5 m away from a tower 25 m high. What is the angle of elevation of the top of the tower from the eye of the observer?
a) 30 degree
b) 60 degree
c) 45 degree
d) 53 degree
View Answer
Explanation: According to the question:
Base = 23.5 m, height = 25 – 1.5 = 23.5 m
Let the angle be x.
➩ Tan x = height / base
➩ Tan x = 23.5 / 23.5
➩ Tan x = 1
➩ x = 45 degree
2. If a tower is 12 m high casts a shadow 4√3 m long on the ground, then what will be the sun’s elevation angle in degree?
a) 60
b) 30
c) 45
d) 90
View Answer
Explanation: Given,
Height = 6 m, base = 2√3 m
Let the angle be x.
➩ tan x = height / base
➩ tan x = 12 / 4√3
➩ tan x = √3
➩ x = 60
3. A kite is flying at the height of 30√3 m from horizontal level. The length of the kite to the person is 60 m. What will be the angle of elevation of the kite?
a) 30 degree
b) 60 degree
c) 37 degree
d) 53 degree
View Answer
Explanation: Let the angle of elevation = x.
Given, height = 30√3 m, hypotenuse = 60m.
➩ sin x = 30√3 / 60
➩ sin x = √3 / 2
➩ x = 60
4. At some time of the day, the length of the shadow of a tower is equal to its height, then what will be the angle of elevation of the sun?
a) 45 degree
b) 30 degree
c) 60 degree
d) 53 degree
View Answer
Explanation: Let the height = h, then the base will be = h.
Let the angle of elevation = x
➩ tan x = h / h
➩ tan x = 1
➩ x = 45 degree
5. The angle of elevation of the top of a tower 60 m high from the foot of another tower in the same plane is 30°, then what will be the distance between the two towers?
a) 20√3 m
b) 60 / √3 m
c) 60√3 m
d) 30 / √3 m
View Answer
Explanation: Given,
Angle = 30, height = 60 m
Let the distance between the 2 towers = x m.
➩ tan 30 = 60 / x
➩ 1 / √3 = 60 / x
➩ x = 60√3
6. The angle of elevation of the top of a tower from point S is 30°. If the observer moves 10 meters towards the tower which is point T, the angle of elevation of the top increases by 15°. What will be the height of the tower?
a) 20 / (√3 – 1) m
b) 20√3 m
c) 10 / √3 m
d) 10 / (√3 – 1) m
View Answer
Explanation: Let the height of the tower = h m.
Point T
Angle = 45, distance = x m
➩ tan 45 = h / x
➩ 1 = h / x
➩ x = h
Point S
Angle = 30, distance = x + 10 m
➩ tan 30 = h / (x + 10)
➩ 1 / √3 = h / (h + 10)
➩ h + 10 = h√3
➩ 10 = h√3 – 1
➩ 10 = h (√3 – 1)
➩ h = 10 / (√3 – 1)
7. If the height of a tower and the distance of the point of observation from its foot, both are increased by 35%, then what will happen to the angle of elevation?
a) Same
b) Increases
c) Decreases
d) No relation
View Answer
Explanation: If the height of a tower and the distance of the point of observation from its foot, both are increased by 35%, then the angle of elevation will remain same.
8. The angle of elevation of the top of a tower from a point on the ground is A. After walking a distance d towards the foot of the tower, angle of elevation is found to be B, then which of the following options is correct with respect to A and B?
a) A = B
b) B < A
c) A < B
d) A = 2B
View Answer
Explanation: A < B is the correct option because as the base distance decreases the angle of elevation increases. Thus, A < B.
9. If the angle of elevation of the top of a tower is 60 degree from a distance of 50 m from the base of the tower, then what will be the height of the tower?
a) 100 / √3 m
b) 50√3 m
c) 50 / √3 m
d) 100√3 m
View Answer
Explanation: Given,
Angle = 60, b = 50 m
Let the height of the tower = h m.
➩ tan 60 = h / b
➩ √3 = h / 50
➩ h = 50√3 m
10. If the angle of elevation of a tower of height 40 m is 30 degree from a point P, then what is the distance of P from the base of the tower?
a) 40√3 m
b) 80 / √3 m
c) 40 / √3 m
d) 80√3 m
View Answer
Explanation: Given,
Angle = 30, h = 40 m
Let the base distance = x m.
➩ tan 30 = h / b
➩ 1 / √3 = 40 / b
➩ b = 40√3 m
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