Height and Distance MCQs

Question 1

A poster is on top of a building. Rajesh is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30° respectively. What is the height of the poster?

Accepted Answer

$$\frac{{50}}{{\sqrt 3 }}\left( {\sqrt 3 - 1} \right)$$

Answer

$$50\sqrt 3 \,{	ext{m}}$$

Answer

$$\frac{{50}}{{\sqrt 3 }}$$

Answer

None of these

Question 2

Angles of elevation of pole are 60° and 45° from points at distances m and n on ground respectively. Here m, when measured from base of pole is less than n. What is the height of the pole?

Accepted Answer

$$\sqrt {mn\sqrt 3 } \,{	ext{units}}$$

Answer

$$\sqrt {mnoot 4 \of 3 } \,{	ext{units}}$$

Answer

$$\sqrt {3mn} \,{	ext{units}}$$

Answer

$$\sqrt {mn} \,{	ext{units}}$$

Question 3

A tree is cut partially and made to fall on ground. The tree however does not fall completely and is still attached to its cut part. The tree top touches the ground at a point 10m from foot of the tree making an angle of 30°. What is the length of the tree?

Accepted Answer

$$10\sqrt 3 \,{	ext{m}}$$

Answer

$$\frac{{10}}{{\sqrt 3 }}\,{	ext{m}}$$

Answer

$$\frac{{\left( {\sqrt 2 - 1} ight)}}{{10}}\,{	ext{m}}$$

Answer

$$\frac{{10}}{{\sqrt 2 }}\,{	ext{m}}$$

Question 4

Tree top’s angle of elevation is 30° from a point on ground, 300m away the tree. When the tree grew up its angle of elevation became 60° from the same point. How much did the tree grow?

Accepted Answer

$${	ext{200}}\sqrt 3 \,{	ext{m}}$$

Answer

$$100\sqrt 3 \,{	ext{m}}$$

Answer

$$300\frac{1}{{\sqrt 3 }}\,{	ext{m}}$$

Answer

$$\frac{{200}}{{\sqrt 3 }}\,{	ext{m}}$$

Question 5

Mohan looks at a tree top and the angle made is 45°. He moves 10 cm back and again looks at the tree top but this time angle made is 30°. How high is the tree top from ground?

Accepted Answer

$$\frac{{10}}{{\sqrt 3 - 1}}\,{	ext{cm}}$$

Answer

$$\frac{{10}}{{\sqrt 3 + 1}}\,{	ext{cm}}$$

Answer

$$20\sqrt 3 \,{	ext{cm}}$$

Answer

$$20\,{	ext{cm}}$$

Question 6

Rohit while seeing a bird on tree top made 45° angle of elevation. He walks 240ft. towards the tree to observe the bird closely, thus making 60° angle of elevation. How far was Rohit from the tree initially?

Accepted Answer

$$\frac{{240\sqrt 3 }}{{\sqrt 3 - 1}}\,{	ext{ft}}$$

Answer

$$\frac{{240}}{{\sqrt 3 - 1}}\,{	ext{ft}}$$

Answer

$$\frac{{240}}{{\sqrt 3 }}\,{	ext{ft}}$$

Answer

$$240\sqrt 3 \,{	ext{ft}}$$

Question 7

A tree breaks and falls to the ground such that its upper part is still partially attached to its stem. At what height did it break, if the original height of the tree was 24 cm and it makes an angle of 30° with the ground?

Accepted Answer

8 cm

Answer

12 cm

Answer

9.5 cm

Answer

7.5 cm

Question 8

Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45° with the ground. How far are the houses from each other if one house is 25m and other is 10m in height?

Accepted Answer

15 m

Answer

18 m

Answer

12 m

Answer

7.5 m

Question 9

Shadow of a man is $$\frac{1}{{\sqrt 3 }}$$ times the height of the man. What will be the sun’s angle of elevation?

Accepted Answer

60°

Answer

135°

Answer

45°

Answer

30°