Practice MCQ Questions and Answer on Height and Distance
91.
If a 1.5 m tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is
- (A) 1.5 m
- (B) 2 m
- (C) 2.5 m
- (D) 2.8 m
92.
As observed from the top a light house, 120ÃÂÃÂÃÂâÃÂÃÂÃÂÃÂ3 m above the sea level, the angle of depression of a ship sailing towards it changes from 30ÃÂÃÂÃÂÃÂÃÂÃÂÃÂð to 60ÃÂÃÂÃÂÃÂÃÂÃÂÃÂð. The distance travelled by the during the period of observation is:
- (A) 240 m
- (B) 240√3 m
- (C) 180√3 m
- (D) 180 m
93.
If the angle of elevation of a tower from a distance of 100 metres from its foot is 60?, the height of the tower is
- (A) $$100\sqrt 3 \,m$$
- (B) $$\frac{{100}}{{\sqrt 3 }}\,m$$
- (C) $$50\sqrt 3 \,m$$
- (D) $$\frac{{200}}{{\sqrt 3 }}\,m$$
94.
Mohan looks at a tree top and the angle made is 45ÃÂÃÂÃÂð. He moves 10 cm back and again looks at the tree top but this time angle made is 30ÃÂÃÂÃÂð. How high is the tree top from ground?
- (A) $$\frac{{10}}{{\sqrt 3 + 1}}\,{\text{cm}}$$
- (B) $$20\sqrt 3 \,{\text{cm}}$$
- (C) $$20\,{\text{cm}}$$
- (D) $$\frac{{10}}{{\sqrt 3 - 1}}\,{\text{cm}}$$
95.
If a 30 m ladder is placed against a 15 m wall such that it just reaches the top of the wall, then the elevation of the wall is equal to-
- (A) 45°
- (B) 30°
- (C) 60°
- (D) 50°
96.
The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30ÃÂÃÂÃÂð with horizontal, then the length of the wire is
- (A) 12 m
- (B) 10 m
- (C) 8 m
- (D) 6 m
97.
From a lighthouse the angles of depression of two ships on opposite sides of the light house are observed to be 30ÃÂÃÂÃÂð and 45ÃÂÃÂÃÂð. If the height of the lighthouse is h metres, the distance between the ships is
- (A) $$\left( {\sqrt 3 + 1} \right)\,h\,{\text{metres}}$$
- (B) $$\left( {\sqrt 3 - 1} \right)\,h\,{\text{metres}}$$
- (C) $$\sqrt 3 \,h\,{\text{metres}}$$
- (D) $${\text{1 + }}\left( {1 + \frac{1}{{\sqrt 3 }}} \right)\,h\,{\text{metres}}$$
98.
A ladder is placed against a wall such that it just reaches the top of the wall. The foot of the ladder is at a distance of 5 metres from the wall. The angle of elevation of the top of the wall from the base of the ladder is 15ÃÂÃÂÃÂð. What is the length (in metres) of the ladder?
- (A) 5√6 - 5√3
- (B) 5√6 - 5√2
- (C) 5√2 - 1
- (D) 5√3 - 5√2
99.
There is a tree between houses of A and B. If the tree leans on AÃÂÃÂÃÂâÃÂÃÂÃÂÃÂs House, the tree top rests on his window which is 12 m from ground. If the tree leans on BÃÂÃÂÃÂâÃÂÃÂÃÂÃÂs House, the tree top rests on his window which is 9 m from ground. If the height of the tree is 15 m, what is distance between AÃÂÃÂÃÂâÃÂÃÂÃÂÃÂs and BÃÂÃÂÃÂâÃÂÃÂÃÂÃÂs house?
- (A) 21 m
- (B) 25 m
- (C) 16 m
- (D) 12 m
100.
The angle of elevation of the top of a tower from a certain point is 30ÃÂÃÂÃÂð. If the observer moves 40 m towards the tower, the angle of elevation of the top of the tower increases by 15ÃÂÃÂÃÂð. The height of the tower is:
- (A) 64.2 m
- (B) 62.2 m
- (C) 52.2 m
- (D) 54.6 m