## Height And Distance Questions MCQs ### Total Questions : 92

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Question 1. A flagstaff is placed on top of a building. The flagstaff and building subtend equal angles at a point on level ground which is 200 m away from the foot of the building. If the height of the flagstaff is 50 m and the height of the building is h, which of the following is true?
1.    h3 - 50h2 + (200)2h + (200)250 = 0
2.    h3 - 50h2 - (200)2h + (200)250 = 0
3.    h3 + 50h2 + (200)2h - (200)250 = 0
4.    None of these
Question 2. From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30° and 60° respectively. What is the height of the pole?
1.    52 m
2.    50 m
3.    66.67 m
4.    33.33 m
Question 3. 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?
1.    $$\frac{{50}}{{\sqrt 3 }}\left( {\sqrt 3 - 1} \right)$$
2.    $$50\sqrt 3 \,{\text{m}}$$
3.    $$50\sqrt 3 \,{\text{m}}$$
4.    None of these
Question 4. 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?
1.    $$\sqrt {mn\sqrt 3 } \,{\text{units}}$$
2.    $$\sqrt {mn\root 4 \of 3 } \,{\text{units}}$$
3.    $$\sqrt {3mn} \,{\text{units}}$$
4.    $$\sqrt {mn} \,{\text{units}}$$
Question 5. 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?
1.    $$10\sqrt 3 \,{\text{m}}$$
2.    $$\frac{{10}}{{\sqrt 3 }}\,{\text{m}}$$
3.    $$\frac{{\left( {\sqrt 2 - 1} \right)}}{{10}}\,{\text{m}}$$
4.    $$\frac{{10}}{{\sqrt 2 }}\,{\text{m}}$$
Question 6. 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?
1.    $$100\sqrt 3 \,{\text{m}}$$
2.    $${\text{200}}\sqrt 3 \,{\text{m}}$$
3.    $$300\frac{1}{{\sqrt 3 }}\,{\text{m}}$$
4.    $$\frac{{200}}{{\sqrt 3 }}\,{\text{m}}$$
Question 7. 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?
1.    $$\frac{{10}}{{\sqrt 3 + 1}}\,{\text{cm}}$$
2.    $$20\sqrt 3 \,{\text{cm}}$$
3.    $$20\,{\text{cm}}$$
4.    $$\frac{{10}}{{\sqrt 3 - 1}}\,{\text{cm}}$$
Question 8. 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?
1.    $$\frac{{240\sqrt 3 }}{{\sqrt 3 - 1}}\,{\text{ft}}$$
2.    $$\frac{{240}}{{\sqrt 3 - 1}}\,{\text{ft}}$$
3.    $$\frac{{240}}{{\sqrt 3 }}\,{\text{ft}}$$
4.    $$240\sqrt 3 \,{\text{ft}}$$
Question 9. 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?
1.    18 m
2.    12 m
3.    7.5 m
4.    15 m
Question 10. 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?
1.    12 cm
2.    8 cm
3.    9.5 cm
4.    7.5 cm
Question 11. Shadow of a man is $$\frac{1}{{\sqrt 3 }}$$ times the height of the man. What will be the sun’s angle of elevation?
1.    135°
2.    45°
3.    30°
4.    60°
Question 12. There is a tree between houses of A and B. If the tree leans on A’s House, the tree top rests on his window which is 12 m from ground. If the tree leans on B’s 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 A’s and B’s house?
1.    21 m
2.    25 m
3.    16 m
4.    12 m
Question 13. Ramesh and Suresh’s mud forts have heights 8 cm and 15 cm. They are 24 cm apart. How far are the fort tops from each other?
1.    31 cm
2.    24 cm
3.    25 cm
4.    24.5 cm
Question 14. A and B are standing on ground 50 meters apart. The angles of elevation for these two to the top of a tree are 60° and 30°. What is height of the tree?
1.    $$50\sqrt 3 \,{\text{m}}$$
2.    $$\frac{{25}}{{\sqrt 3 }}\,{\text{m}}$$
3.    $$25\sqrt 3 \,{\text{m}}$$
4.    $$\frac{{25}}{{\sqrt 3 - 1}}\,{\text{m}}$$
Question 15. There is a tower of 10m between two parallel roads. The angles of depression of the roads from the top of the tower are 30° and 45°. How far are the roads from each other?
1.    27.32 m
2.    29.56 m
3.    $$20\sqrt 3 \,{\text{m}}$$
4.    $$\frac{{10}}{{\sqrt 3 }}\,{\text{m}}$$
Question 16. Raj stands in a corner of his square farm. Angle of elevation of a scarecrow placed in diagonally opposite corner is 60°. He starts walking backwards in a straight line and after 80ft he realizes that angle of elevation of the scarecrow now is 30°. What is area of the field?
1.    1600 sq.ft.
2.    40 sq.ft.
3.    $$\frac{{40}}{{\sqrt 2 }}$$ sq.ft.
4.    800 sq.ft.
Question 17. Due to sun, a 6ft man casts a shadow of 4ft, whereas a pole next to the man casts a shadow of 36ft. What is the height of the pole?
1.    63 ft
2.    72 ft
3.    54 ft
4.    48 ft
Question 18. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
1.    173 m
2.    200 m
3.    273 m
4.    300 m
5.    None of these