Height And Distance(Quantitative Aptitude ) Questions and answers for exam Preparation

Quantitative Aptitude

HEIGHT AND DISTANCE MCQs

Total Questions : 206 | Page 6 of 21 pages

Question 51. The angles of depression of two ships from the top of a light house are 45° and 30° towards east. If the ships are 100 m apart, the height of the light house is

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

Discuss Question

Answer: Option C. -> $$50\left( {\sqrt 3 - 1} \right)m$$

Question 52. If the angles of elevation of a tower from two points distance a and b (a > b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is?

$$\sqrt {a + b} $$
$$\sqrt {ab} $$
$$\sqrt {a - b} $$
$$\sqrt {\frac{a}{b}} $$

Discuss Question

Answer: Option B. -> $$\sqrt {ab} $$

Question 53. A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is

$$15\sqrt 3 \,m$$
$$\frac{{15\sqrt 3 }}{2}\,m$$
$$\frac{{15}}{2}\,m$$
$$15\,m$$

Discuss Question

Answer: Option B. -> $$\frac{{15\sqrt 3 }}{2}\,m$$

Question 54. Two poles are ‘a’ metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is

$$\sqrt {2a} \,{\text{metres}}$$
$$\frac{a}{{2\sqrt 2 }}\,{\text{metres}}$$
$$\frac{a}{{\sqrt 2 }}\,{\text{metres}}$$
$$2a\,{\text{metres}}$$

Discuss Question

Answer: Option B. -> $$\frac{a}{{2\sqrt 2 }}\,{\text{metres}}$$

Question 55. From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is

25 m
50 m
75 m
100 m

Discuss Question

Answer: Option B. -> 50 m

Question 56. The angle of elevation of the top of a tower at a point on the ground 50 m away from the foot of the tower is 45°. Then the height of the tower (in metres) is

$$50\sqrt 3 $$
$$50$$
$$\frac{{50}}{{\sqrt 2 }}$$
$$\frac{{50}}{{\sqrt 3 }}$$

Discuss Question

Answer: Option B. -> $$50$$

Question 57. The ratio of the length of a rod and its shadow is 1 : $$\sqrt 3 $$ The angle of elevation of the sum is

30°
45°
60°
90°

Discuss Question

Answer: Option A. -> 30°

Question 58. A ladder makes an angle of 60° with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is

$$\frac{4}{{\sqrt 3 }}$$
$$4\sqrt 3 $$
$$2\sqrt 2 $$
$$4$$

Discuss Question

Answer: Option D. -> $$4$$

Question 59. It is found that on walking x metres towards a chimney in a horizontal line through its base, the elevation of its top changes from 30° to 60° . The height of the chimney is

$$3\sqrt 2 \,x$$
$$2\sqrt 3 \,x$$
$$\frac{{\sqrt 3 }}{2}\,x$$
$$\frac{2}{{\sqrt 3 }}\,x$$

Discuss Question

Answer: Option C. -> $$\frac{{\sqrt 3 }}{2}\,x$$

Question 60. A lower subtends an angle of 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60°. The height of the tower is