This set of Aptitude Questions and Answers (MCQs) focuses on “Height and Distance – Set 4”.
1. 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 is the length of the ladder?
a) 16 m
b) 15 m
c) 12 m
d) 8 m
View Answer
Explanation: Given,
Angle = 60 – degree, base distance = 6 m
Let the length of the ladder be = h m.
➩ cos 60 = base distance / length of ladder
➩ 1 / 2 = 6 / h
➩ h = 12 m
2. The shadow of a building is 8 m long when the sun is at an angle of elevation of 30 degree. What will be the height of the building?
a) 8 / √3 m
b) 6 / √3 m
c) 8√3 m
d) 12√3 m
View Answer
Explanation: Given,
Angle = 30 – degree, base distance = 8 m
Let the height of the building be = h m.
➩ tan 30 = height of building / base distance
➩ 1 / √3 = h / 8
➩ h = 8 / √3 m
3. When the sun’s altitude changes from 30 to 60 degree, the length of the shadow of a pole decreases by 150 m. What is the original length of the shadow?
a) 150 m
b) 225 m
c) 275 m
d) 180 m
View Answer
Explanation: Given,
Original angle = 30 – degree, new angle = 60 degree
Let the original length of the shadow be = x m, new length = x – 150 m, height of the pole = h m.
Original angle
➩ tan 30 = height / base length
➩ 1 / √3 = h / x
➩ x = h√3 m
New angle
➩ tan 60 = height / base length
➩ √3 = h / x – 150
➩ √3(x – 150) = h
Substituting this value of h in first equation:
➩ x = h√3
➩ x = (√3(x – 150)) * √3
➩ x = 3x – 450
➩ 450 = 2x
➩ x = 225 m
4. The angle of elevation of a cloud from a point 300 m above a lake is 30 degree and the angle of depression of its reflection in the lake is 60 degree. What will be the height of the cloud?
a) 300 m
b) 250 m
c) 200 m
d) 350 m
View Answer
Explanation: Let the height of the cloud be h m and base distance be b m.
➩ tan 30 = height / base distance
➩ 1 / √3 = h / b
➩ b = h√3
According to the question:
➩ tan 60 = height / base distance
➩ √3 = (h + 300 + 300) / b
Substituting the value of b in terms of h from the above equation
➩ √3 = (h + 600) / h√3
➩ 3h = h + 600
➩ 2h = 600
➩ h = 300 m
5. The tops of two poles of height 40 m and 30 m are connected by a wire. If the wire makes an angle of 60 degree with the horizontal, then what will be the length of the wire used?
a) 20 / √3 m
b) 10√3 m
c) 20 m
d) 12 / √3 m
View Answer
Explanation: Let the length of the wire = x m.
According to the question:
➩ sin 30 = height difference / length of wire
➩ 1 / 2 = 10 / x
➩ x = 20 m
6. A straight tree is broken due to thunder storm. The broken part is bent in such a way that the peak touches the ground at an angle elevation of 53°. The peak of the tree touches the ground at a distance of 15 m. What will be the height of the tree?
a) 68.52 m
b) 55.76 m
c) 58.62 m
d) 64.58 m
View Answer
Explanation: Given,
Angle = 53 – degree, base distance = 15 m
Let the vertical height be = x m, diagonal length be = y m.
➩ tan 53 = vertical height / base distance
➩ 4 / 3 = x / 25
➩ x = 100 / 3 m = 33.33 m
Also,
➩ sin 53 = vertical height / perpendicular distance
➩ 4 / 5 = 25 / y
➩ y = 125 / 4 m = 31.25 m
Height of the tree = x + y
= 33.33 + 31.25 m
= 64.58 m
7. A kite is flying at a vertical height of 300 m making an angle of depression of 60 degree. What will be the length of thread required in this case?
a) 600 / √3 m
b) 300√3 m
c) 1200 / √3 m
d) 600 / √2 m
View Answer
Explanation: Given,
Angle = 60 – degree, height = 300 m
Let the length of thread (diagonal) = d m.
➩ sin 60 = height / diagonal
➩ √3 / 2 = 300 / d
➩ d = 600 / √3 m
8. A stone rolls down a slope having vertical height and base distance equal to 60 m. What will be the length of the slope?
a) 30√3 m
b) 120 / √3 m
c) 60√2 m
d) 60 / √2 m
View Answer
Explanation: Given,
Vertical height = 60 m, base distance = 60 m
Let the angle = A, slope length = h m.
➩ tan A = vertical height / base distance
➩ tan A = 60 / 60
➩ A = 45
Now,
➩ Sin 45 = vertical height / slope length
➩ 1 / √2 = 60 / h
➩ h = 60√2 m
9. A bus took 60 seconds to drive down a slopy hill of height 600 m. If the angle of depression of the path is 30 degree, then what was the speed of the bus?
a) 20 m / s
b) 20 / √2 m / s
c) 10√2 m / s
d) 20 / 3 m / s
View Answer
Explanation: Given,
Angle = 30 – degree, time = 60 seconds, height = 600 m.
Let the length of the path = h m.
➩ sin 30 = height / length of path
➩ \(\frac {1}{2}\) = 600 / h
➩ h = 1200 m
Speed = distance / time
➩ Speed = 1200 m / 60 sec
➩ Speed = 20 m / s
10. If the height of a tower and the distance of the point of observation are both halved, then what will happen to the angle of depression?
a) Same
b) Increases
c) Decreases
d) No relation
View Answer
Explanation: Option same is correct as 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.
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