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
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
Go to :
Total Pages : 13