Height and Distance Questions and answers

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
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). \( \Large \sqrt{a-b} \)
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). \( \Large \frac{1}{3} \)
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). \( \Large \left(\sqrt{3} - 2\right) km \)
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
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


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). \( \Large 600(\sqrt{3}-1) \)
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
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). \( \Large \frac{h\ coty}{cotx-coty} \)
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). \( \Large 20\sqrt{3}m \)
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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