This set of Aptitude Questions and Answers (MCQs) focuses on “Angle of Elevation”.
1. If the length of the shadow of a building is increasing, then what will happen to the angle of elevation to the sun?
a) Reduces to zero
b) Increase
c) Decrease
d) Becomes double
View Answer
Explanation: If the length of the shadow of a building is increasing, then the angle of elevation to the sun keeps decreasing.
2. The angle of elevation of the top of a pole is 30 degree. If the height of the pole is doubled, then what will happen to the angle of elevation to its top?
a) < 60
b) Doubled
c) Halved
d) Same
View Answer
Explanation: Let the height of the building be h and the base distance be b.
➩ tan 30 = h / b
➩ 1 / √3 = h / b
➩ h = b / √3
Now height is doubled.
➩ tan x = 2h / b
➩ tan x = 2 / b * b / √3
➩ tan x = 2 / √3
Thus, x < 60.
3. If the height of the tower and the base distance both are doubled, then what will happen to the elevation angle?
a) Doubled
b) Same
c) Halved
d) Four times
View Answer
Explanation: If the height of the tower and the base distance both are doubled, then the angle of elevation will remain same.
4. A 20 m ladder just reaches the top of a pole by making an angle of elevation of 30 degree. What will be the height of the pole?
a) 10 m
b) 15 m
c) 20 m
d) 25 m
View Answer
Explanation: Given,
Angle of elevation = 30, hypotenuse = 20 m, height of pole = X m
➩ sin 30 = p / h
➩ \(\frac {1}{2}\) = X / 20
➩ X = 10 m
5. If at some time, the length of the shadow of a building is √3 times its height, then what will be the angle of elevation of the building in degree, at that time?
a) 37
b) 45
c) 30
d) 60
View Answer
Explanation: Let the height of the building be h.
Then, length of shadow = h√3.
Angle of elevation = tan x
➩ tan x = h / (h√3)
➩ tan x = 1 / √3
➩ x = 30 degree
6. If the height of a tower is 10 m and the angle a ladder that just touches its top makes with the base land is 45 degree, then what will be the base distance?
a) 10√3 m
b) 5 m
c) 20 m
d) 10 m
View Answer
Explanation: Given,
Height = 10 m, angle of elevation = 45, base distance = b
Tan 45 = h / b
➩ 1 = 10 / b
➩ b = 10 m
7. What will be the angle of elevation of the top of a 12 m high building at a point 12√3 m away from the base?
a) 30 degree
b) 60 degree
c) 45 degree
d) 53 degree
View Answer
Explanation: Given,
Height = 12 m, base = 12√3 m
Let the angle of elevation be x.
➩ tan x = height / base
➩ tan x = 12 / 12√3
➩ tan x = 1 / √3
➩ x = 30
8. The angle of elevation of a ladder leaning against a wall is 60 degree and the foot of the ladder is 6 m away from the wall. What will be the length of the ladder?
a) 12 / √3 m
b) 6√3 m
c) 12 m
d) 12√3 m
View Answer
Explanation: Given,
Angle of elevation = 60, base = 6m.
Let the length of the ladder = l
➩ Cos 60 = base / l
➩ \(\frac {1}{2}\) = 6 / l
➩ l = 12m
9. The angles of elevation of the top of a tower from two points at distant of s and r m from its foot are complementary. What will be the height of this tower?
a) 2sr
b) √sr
c) sr / 2
d) 2sr / 3
View Answer
Explanation: Let the angle of elevation from point at s be A so the angle of elevation at r distance will be 90 – B and let the height of the tower be h.
➩ tan A = h / s
➩ tan (90 – A) = h / r
➩ cot A = h / r
On multiplying,
➩ tan A * cot A = h / s * h / r
➩ 1 = h2 / sr
➩ h = √sr
10. If the shadow of a tower is √3 times the height of the tower, then what is the sun’s altitude at this time in degree?
a) 30
b) 45
c) 60
d) 0
View Answer
Explanation: Let the height of the tower be h.
Then length of shadow = h√3.
Tan A = h / h√3
= 1 / √3
Thus, A = 30 degree.
To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.
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