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Quantitative Aptitude

HEIGHT AND DISTANCE MCQs

Total Questions : 206 | Page 5 of 21 pages
Question 41. A man is watching from the top of 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 meters 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?
  1.    32 kmph
  2.    36 kmph
  3.    38 kmph
  4.    40 kmph
  5.    42 kmph
 Discuss Question
Answer: Option A. -> 32 kmph
Question 42. The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of electric pole ?
  1.    5 meters
  2.    8 meters
  3.    10 meters
  4.    12 meters
  5.    None of these
 Discuss Question
Answer: Option C. -> 10 meters
Question 43. TF is a tower with F on the ground. The angle of elevation of T from A is x° such that tan x°= $$\frac{2}{5}$$   and AF = 200 m. The angle of elevation of T from a nearer point B is y° with BF = 80 m. The value of y° is-
  1.    75°
  2.    45°
  3.    60°
  4.    30°
 Discuss Question
Answer: Option B. -> 45°
Question 44. From a lighthouse the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the lighthouse is h metres, the distance between the ships is
  1.    $$\left( {\sqrt 3 + 1} \right)\,h\,{\text{metres}}$$
  2.    $$\left( {\sqrt 3 - 1} \right)\,h\,{\text{metres}}$$
  3.    $$\sqrt 3 \,h\,{\text{metres}}$$
  4.    $${\text{1 + }}\left( {1 + \frac{1}{{\sqrt 3 }}} \right)\,h\,{\text{metres}}$$
 Discuss Question
Answer: Option A. -> $$\left( {\sqrt 3 + 1} \right)\,h\,{\text{metres}}$$
Question 45. From the top of a tower, the angles of depression of two objects P and Q (situated on the ground on the same side of the tower) separated at a distance of 100$${\left( {3 - \sqrt 3 } \right)}$$   m are 45° and 60 ° respectively. The height of the tower is-
  1.    200 m
  2.    250 m
  3.    300 m
  4.    None of these
 Discuss Question
Answer: Option C. -> 300 m
Question 46. 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
  1.    1.5 m
  2.    2 m
  3.    2.5 m
  4.    2.8 m
 Discuss Question
Answer: Option C. -> 2.5 m
Question 47. If the height of a vertical pole is $$\sqrt 3 $$ times the length of its shadow on the ground, then the angle of elevation of the sun at that time is
  1.    30°
  2.    60°
  3.    45°
  4.    75°
 Discuss Question
Answer: Option B. -> 60°
Question 48. Two persons are 'a' meters apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter post is
  1.    $$\frac{a}{4}$$
  2.    $$\frac{a}{{\sqrt 2 }}$$
  3.    $$a\sqrt 2 $$
  4.    $$\frac{a}{{2\sqrt 2 }}$$
 Discuss Question
Answer: Option D. -> $$\frac{a}{{2\sqrt 2 }}$$
Question 49. 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
  1.    $$100\sqrt 3 \,m$$
  2.    $$\frac{{100}}{{\sqrt 3 }}\,m$$
  3.    $$50\sqrt 3 \,m$$
  4.    $$\frac{{200}}{{\sqrt 3 }}\,m$$
 Discuss Question
Answer: Option A. -> $$100\sqrt 3 \,m$$
Question 50. The angle of depression of a car, standing on the ground, from the top of a 75 m tower, is 30°. The distance of the car from the base of the tower (in metres) is
  1.    25 $$\sqrt 3 $$
  2.    50 $$\sqrt 3 $$
  3.    75 $$\sqrt 3 $$
  4.    150
 Discuss Question
Answer: Option C. -> 75 $$\sqrt 3 $$

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