# Height and Distance Questions and answers

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1). The angle of elevation of the top of a tower at a point on the ground is $$\Large 30 ^{\circ}$$. If on walking 20m towards the tower the angle of elevation becomes $$\Large 60 ^{\circ}$$ then the heights of the tower is:
 A). 10 m B). $$\Large \frac{10}{\sqrt{3}} m$$ C). $$\Large 10\sqrt{3} m$$ D). None of these
2). When the elevation of sun changes from $$\Large 45 ^{\circ}$$ to $$\Large 30 ^{\circ}$$ the shadow of a tower increases by 60 m, The height of the tower is:
 A). $$\Large 30\sqrt{3} m$$ B). $$\Large 30 \left(\sqrt{2} + 1\right) m$$ C). $$\Large 30 \left(\sqrt{3} - 1\right) m$$ D). $$\Large 30 \left(\sqrt{3} + 1\right) m$$
3). A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $$\Large 60 ^{\circ}$$ when he retire 40 m from the bank he finds the angle to be $$\Large 30 ^{\circ}$$. The breadth of the river is:
 A). 20 m B). 40 m C). 30 m D). 60 m
4). A flag-staff is upon the top of a building. If at a distance of 40 m from the base of building the angles of elevation of the tapes of the flag-staff and building are $$\Large 60 ^{\circ}$$ and $$\Large 30 ^{\circ}$$ respectively, then the height of the flag-staff is:
 A). 46.19 m B). 50 m C). 25 m D). none of these
5). A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window be 64 m, the distance between the two houses is:
 A). 48 m B). 36 m C). 54 m D). 72 m

6). From the top of a light house 60 m high with its base at the sea level the angle of depression of a boat is $$\Large 15 ^{\circ}$$. The distance of the boat from the foot of light house is:
 A). $$\Large \left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)60 m$$ B). $$\Large \frac{\sqrt{3+1}}{\sqrt{3-1}} m$$ C). $$\Large \left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)60 m$$ D). none of therse
7). Two poles of equal heights stand on either side of a 100 m wide road. At a point between the poles the angles of elevation of the tops of the poles are $$\Large 30 ^{\circ}$$ and $$\Large 60 ^{\circ}$$. The height of each pole is:
 A). 25m B). $$\Large 25\sqrt{3} m$$ C). $$\Large \frac{100}{\sqrt{3}} m$$ D). none of these
8). At a distance 2h metre from the foot of a tower of height h meter the top of the tower and pole at the top of tower subtend equal angles. Height of the pole should be
 A). $$\Large \frac{5h}{3} m$$ B). $$\Large \frac{4h}{3} m$$ C). $$\Large \frac{7h}{3} m$$ D). $$\Large \frac{3h}{3} m$$
9). A kite is flying at an inclination of $$\Large 60 ^{\circ}$$ with the horizontal. If the length of the thread is 120 m, then the height of the kite is:
 A). $$\Large 60\sqrt{3} m$$ B). 60 m C). $$\Large \frac{60}{\sqrt{3}} m$$ D). 120 m
10). If a flag staff of 6 m high placed on the top of a tower throws a $$\Large 2\sqrt{3} m$$ along the ground, then the angle (in degrees) that the sun makes with the ground is:
 A). $$\Large 60 ^{\circ}$$ B). $$\Large 80 ^{\circ}$$ C). $$\Large 75 ^{\circ}$$ D). none of these
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