# Height And Distance – Aptitude MCQ Questions – 07

Question 1
Rohit while seeing a bird on tree top made 45Â° angle of elevation. He walks 240ft. towards the tree to observe the bird closely, thus making 60Â° angle of elevation. How far was Rohit from the tree initially?

 Â Â Â A. 240âˆš3/âˆš3âˆ’1 ft Â Â Â B. 240/âˆš3âˆ’1 ft Â Â Â C. 240/âˆš3 ft Â Â Â D. 240âˆš3 ft

Question 2
Mohan looks at a tree top and the angle made is 45Â°. He moves 10 cm back and again looks at the tree top but this time angle made is 30Â°. How high is the tree top from ground?

 Â Â Â A. 10/âˆš3+1cm Â Â Â B. 20âˆš3 cm Â Â Â C. 20 cm Â Â Â D. 10/âˆš3âˆ’1cm

Question 3
Tree topâ€™s angle of elevation is 30Â° from a point on ground, 300m away the tree. When the tree grew up its angle of elevation became 60Â° from the same point. How much did the tree grow?

 Â Â Â A. 100âˆš3 m Â Â Â B. 200âˆš3 m Â Â Â C. 300*1/âˆš3 m Â Â Â D. 200/âˆš3 m

Question 4
From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30Â° and 60Â° respectively. What is the height of the pole?

 Â Â Â A. 52 m Â Â Â B. 50 m Â Â Â C. 66.67 m Â Â Â D. 33.33 m

Question 5
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 30Â° with the ground?

 Â Â Â A. 12 cm Â Â Â B. 8 cm Â Â Â C. 9.5 cm Â Â Â D. 7.5 cm

Question 6
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?

 Â Â Â A. h3 - 50h2 + (200)2h + (200)250 = 0 Â Â Â B. h3 - 50h2 - (200)2h + (200)250 = 0 Â Â Â C. h3 + 50h2 + (200)2h - (200)250 = 0 Â Â Â D. None of these

Question 7
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 30Â°. What is the length of the tree?

 Â Â Â A. $$10\sqrt 3 \,{\text{m}}$$ Â Â Â B. $$\frac{{10}}{{\sqrt 3 }}\,{\text{m}}$$ Â Â Â C. $$\frac{{\left( {\sqrt 2 - 1} \right)}}{{10}}\,{\text{m}}$$ Â Â Â D. $$\frac{{10}}{{\sqrt 2 }}\,{\text{m}}$$

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 45Â° with the ground. How far are the houses from each other if one house is 25m and other is 10m in height?

 Â Â Â A. 18 m Â Â Â B. 12 m Â Â Â C. 7.5 m Â Â Â D. 15 m

Question 9
Angles of elevation of pole are 60Â° and 45Â° 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?

 Â Â Â A. $$\sqrt {mn\sqrt 3 } \,{\text{units}}$$ Â Â Â B. $$\sqrt {mn\root 4 \of 3 } \,{\text{units}}$$ Â Â Â C. $$\sqrt {3mn} \,{\text{units}}$$ Â Â Â D. $$\sqrt {mn} \,{\text{units}}$$

Question 10
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 45Â° and 30Â° respectively. What is the height of the poster?

 Â Â Â A. $$\frac{{50}}{{\sqrt 3 }}\left( {\sqrt 3 - 1} \right)$$ Â Â Â B. $$50\sqrt 3 \,{\text{m}}$$ Â Â Â C. $$50\sqrt 3 \,{\text{m}}$$ Â Â Â D. None of these