1000+ How to Solve Heights and Distance Problems - 1

Question: 1

A person walking along a straight road towards a hill observes at two points, distance √3 Km, the angles of elevation of the hill to be 30° and 60°. The height of the hill is

(A) $${3}/{2}$$ km

(B) $$√2$$

(C) $${5}/{2}$$

(D) $$√3$$

Ans: A

Question: 2

A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man’s eye when at a distance of 60 metres from the tower. After 5 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?

(A) 32 kmph

(B) 36 kmph

(C) 38 kmph

(D) 42 kmph

Ans: A

Question: 3

When the sun is 30° above the horizontal;, the length of shadow cast by a building 50 m high is

(A) 25 m

(B) 50 m

(C) 50 $$√3$$

(D) 70 $$√3$$

Ans: C

Question: 4

In a rectangle, if the angle between a diagonal and a side is 30° and the length of diagonal is 6 cm, the area of the rectangle is

(A) 9 cm²

(B) 9 $$√3$$ cm²

(C) 12 cm²

(D) 14 cm²

Ans: B

Question: 5

A pole being broken by the wind, the top struck the ground at an angle of 30° and at a distance of 21 m from the foot of the pole. Find out the total height of the pole

(A) 19 m

(B) 21$$√3$$ m

(C) 23 m

(D) 25 m

Ans: B