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
21). What is the angle of elevation of the Sun when the shadow of a pole is \( \Large \sqrt{3} \) times the length of the pole?
A). \( \Large 30 ^{\circ} \)
B). \( \Large 45 ^{\circ} \)
C). \( \Large 60 ^{\circ} \)
D). None of these
22). The shadow of a tower is 15 m, when the Sun's elevation is \( \Large 30 ^{\circ} \). What is the length of the shadow, when the Sun's elevation is \( \Large 60 ^{\circ} \)?
A). 3m
B). 4m
C). 5m
D). 6m
23). What is the angle of elevation of the Sun. when the shadow of a pole of height x m is \( \Large \frac{x}{\sqrt{3}} \)
A). \( \Large 30 ^{\circ} \)
B). \( \Large 45 ^{\circ} \)
C). \( \Large 60 ^{\circ} \)
D). \( \Large 75 ^{\circ} \)
24). A vertical stick 12 In long casts a shadow 8 m long on the ground. At the same time, a tower casts a shadow of 40m long on the ground. The height of the tower is
A). 60 m
B). 65 m
C). 70 m
D). 72 m
25). The tops of two poles of height 24 m and 36 m are connected by a wire. If the wire makes an angle of \( \Large 60 ^{\circ} \) with the horizontal, then the length of the wire is
A). \( \Large 8\sqrt{3} \) m
B). 8m
C). \( \Large 6\sqrt{3} \) m
D). 6m


26). The shadow of a tower standing on a level plane is found to be 50 m longer when the Sun's elevation is \( \Large 30 ^{\circ} \). When it is \( \Large 60 ^{\circ} \), then what is the height of the tower?
A). 25m
B). \( \Large 25\sqrt{3} \) m
C). \( \Large \frac{25}{\sqrt{3}} \)
D). 30m
27). The angle of elevation of the tip of a tower from a point on the ground is \( \Large 45 ^{\circ} \). Moving 21 m directly towards the base of the tower, the angle of elevation changes to \( \Large 60 ^{\circ} \). What is the height of the tower, to the nearest metre?
A). 48 m
B). 49 m
C). 50 m
D). 51 m
28). The angles of depression from the top of a light house of two boats are \( \Large 45 ^{\circ} \) and \( \Large 30 ^{\circ} \) towards the west. If the two boats are 5 m apart, then the height of the light house is
A). \( \Large \left(2.5\sqrt{3}-1\right) m \)
B). \( \Large 2.5 \left(\sqrt{3}-1\right) m \)
C). \( \Large \left(2.5\sqrt{3}+1\right) m \)
D). \( \Large 2.5 \left(\sqrt{3}+1\right) m \)
29). The angle of elevation of the top of an unfinished pillar at a point 150m from its base is \( \Large 30 ^{\circ} \). If the angle of elevation at the same point is to be \( \Large 45 ^{\circ}  \), then the pillar has to be raised to a height of how many meters?
A). 59.4m
B). 61.4m
C). 62.4m
D). 63.4m
30). From the top of a cliff 200 m high, the angles of depression of the top and bottom of a tower are observed to be \( \Large 30 ^{\circ} \) and \( \Large 45 ^{\circ} \), respectively. What is the height of the tower?
A). 400 m
B). \( \Large 400\sqrt{3} \) m
C). \( \Large \frac{400}{\sqrt{3}} \) m
D). None of these
Go to :
Total Pages : 13