Height & Distance Practice Problems: Level 01

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Directions: Solve the following questions applying the various surds and indices formulas.
Q.1.A tower standing on a horizontal plane makes an angle α at a point which is 160m apart from the foot of the tower. On moving 100m towards the base of the tower, the angle of elevation becomes 2α. Find the height of the tower.
a) 100m
b) 80m
c) 120m
d) 90m
Q.2. A man is standing on a corner of a square field. He observes that the angle of elevation of the top of a pole in the corner just diagonally opposite to this corner is 600. When he moves 100√2m from the corner along the same straight line (along the diagonal joining the two corners in question), he finds that the angle is 300. Find the area of the field.
a) 100m2
b) 2500m2
c) 1600m2
d) 1200m2
Q.3. From the top of a hill 120m high, the angle of depression of top and bottom of a tower are 450 and 600 respectively, find the height of the tower.
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a) 40.83m
b) 63.12m
c) 77.14m
d) 50.72m
Q.4.Two boats are sailing in the sea on the two opposite sides of a light house 50m high. The angles of elevation of the top of the light house observed from the ships are 300 and 450 respectively. Find the distance between the two ships.
a) 136.6m
b) 142.8m
c) 150.4m
d) 122.8m
Q.5.A man 1.5m tall is 10√3m away from the pole. The angle of elevation from his eye to the top of the tower is 600. Find the height of the tower.
a) 31.5m
b) 36.7m
c) 24.8m
d) 28.6m
Q6.When the sun’s altitude changes from 300 to 600, the length of the shadow of a building decreases by 40m. What is the height of the building?
a) 22√3
b) 15√3
c) 16√2
d) 20√3
Q.7.A man standing at a point A, observes that the angles of elevation of two planes one vertically above the other are 600 and 300. If the higher plane is 1200m from the ground, find the vertical distance between the two planes.
a) 650m
b) 800m
c) 900√3m
d) 1000√3m
Q8.A tower is surmounted by a vertical flag post of height 20m. At a point on the ground, the angle of elevation of the bottom and the top of the flag post are 300 and 600 respectively. Find the height of the tower.
a) 10m
b) 12m
c) 16m
d) 18m
Q9.A balloon leaves from a point A vertically upward at uniform speed. A man standing 200m away from point A observes the angle of elevation of the balloon to be 600 after 3 minutes. Find the speed of the balloon.
a) 2.423m/s
b) 1.924m/s
c) 1.863m/s
d) 2.875m/s
Q10.The angles of depression and elevation of the top of a building 15m high from the top and bottom of a tower are 600 and 300 respectively. Find the height of the tower
a) 40m
b) 50m
c) 60m
d) 80m
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