Lakshya Education MCQs

Question: 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
Options:
 A. $$50\sqrt 3$$ B. $$50$$ C. $$\frac{{50}}{{\sqrt 2 }}$$ D. $$\frac{{50}}{{\sqrt 3 }}$$

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Question 1. The ratio of the length of a rod and its shadow is 1 : $$\sqrt 3$$ The angle of elevation of the sum is
1.    30°
2.    45°
3.    60°
4.    90°
Question 2. 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
1.    $$\frac{4}{{\sqrt 3 }}$$
2.    $$4\sqrt 3$$
3.    $$2\sqrt 2$$
4.    $$4$$
Question 3. 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
1.    $$3\sqrt 2 \,x$$
2.    $$2\sqrt 3 \,x$$
3.    $$\frac{{\sqrt 3 }}{2}\,x$$
4.    $$\frac{2}{{\sqrt 3 }}\,x$$
Question 4. 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
1.    25 m
2.    50 m
3.    75 m
4.    100 m
Question 5. 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
1.    $$\sqrt {2a} \,{\text{metres}}$$
2.    $$\frac{a}{{2\sqrt 2 }}\,{\text{metres}}$$
3.    $$\frac{a}{{\sqrt 2 }}\,{\text{metres}}$$
4.    $$2a\,{\text{metres}}$$
1.    $$15\sqrt 3 \,m$$
2.    $$\frac{{15\sqrt 3 }}{2}\,m$$
3.    $$\frac{{15}}{2}\,m$$
4.    $$15\,m$$