41). If the angle of elevation of a tower from two distant points a and b (a > b) from its foot and In the same straight line and on the same side of it are \( \Large 30 ^{\circ} \) and \( \Large 60 ^{\circ} \), then the height of the tower is
A). \( \Large \sqrt{\frac{a}{b}} \) |
B). \( \Large \sqrt{a+b} \) |
C). \( \Large \sqrt{ab} \) |
D). \( \Large \sqrt{a-b} \) |
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42). The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is \( \Large 60 ^{\circ} \), and the angle of elevation of the top of the second tower from the foot of the first tower is \( \Large 30 ^{\circ} \). The distance between the two towers is n times the height of the shorter tower. What is n equal to?
A). \( \Large \sqrt{2} \) |
B). \( \Large \sqrt{3} \) |
C). \( \Large \frac{1}{2} \) |
D). \( \Large \frac{1}{3} \) |
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43). At the foot of a mountain, the elevation of its summit is \( \Large 45 ^{\circ} \). After ascending 2km towards the mountain upon an incline of \( \Large 30 ^{\circ} \), the elevation changes to \( \Large 60 ^{\circ} \). The height of the mountain is
A). \( \Large \left(\sqrt{3} - 1\right) km \) |
B). \( \Large \left(\sqrt{3} + 1\right) km \) |
C). \( \Large \left(\sqrt{3} + 2\right) km \) |
D). \( \Large \left(\sqrt{3} - 2\right) km \) |
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44). A man standing in one corner of a square football field observes that the angle subtended by a pole in the corner just diagonally opposite to this corner is \( \Large 60 ^{\circ} \). When he retires 80 m from the corner, along the same straight line, he finds the angle to be \( \Large 30 ^{\circ} \). The length of the field is
A). 20 m |
B). \( \Large 40\sqrt{2} \) m |
C). 40 m |
D). \( \Large 20\sqrt{2} \) m |
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45). A spherical balloon of radius r subtends angle \( \Large 60 ^{\circ} \) at the eye of an observer. If the angle of elevation of its centre is \( \Large 60 ^{\circ} \) and h is the height of the centre of the balloon, then which one of the following is correct?
A). h=r |
B). \( \Large h = \sqrt{2}r \) |
C). \( \Large h = \sqrt{3}r \) |
D). h=2r |
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46). The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, then the speed of the aeroplane in km/ hr. is
A). \( \Large 600 \) |
B). \( \Large 600(\sqrt{3}+1) \) |
C). \( \Large 600\sqrt{3} \) |
D). \( \Large 600(\sqrt{3}-1) \) |
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47). At a point on a horizontal line through the base of a monument the angle of elevation of the top of the monument is found to be such that its tangent is \( \Large \frac{1}{5} \) On walking 138 metres towards the monument the secant of the angle of elevation is found to be \( \Large \frac{\sqrt{193}}{12} \). The height of the monument (in metre) is
A). 42 |
B). 49 |
C). 35 |
D). 56 |
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48). The angle of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h metre, then the height of the building is (in metre)
A). \( \Large \frac{h\ cotx}{cotx+coty} \) |
B). \( \Large \frac{h\ coty}{cotx+coty} \) |
C). \( \Large \frac{h\ cotx}{cotx-coty} \) |
D). \( \Large \frac{h\ coty}{cotx-coty} \) |
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49). The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 metres towards the foot: of the tower to a point B, the angle of elevation increases to 60°. The height of the tower is
A). \( \Large \sqrt{3}m \) |
B). \( \Large 5\sqrt{3}m \) |
C). \( \Large 10\sqrt{3}m \) |
D). \( \Large 20\sqrt{3}m \) |
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50). Two poles of equal height are standing opposite to each other on either side of a road which is 100m wide. From a point between them on road, angle of elevation of their tops are 30° and 60°. The height of each pole ( in meter) is
A). \( \Large 25\sqrt{3} \) |
B). \( \Large 20\sqrt{3} \) |
C). \( \Large 28\sqrt{3} \) |
D). \( \Large 30\sqrt{3}m \) |
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