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>> Elementary Mathematics >> Height and Distance
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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