 # Height & Distance Practice Problems : Level 02

Directions: Solve the following questions applying the various surds and indices formulas.
Q.1.A man is standing on the deck of a ship, which is 10m above water level. He observes the angle of elevation of the top of a light house as 600 and the angle of depression of the base of lighthouse as 300. Find the height of the light house.
a) 30m
b) 40m
c) 45m
d) 38m
Q.2. A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 450. When he moves 20m away from the bank, he finds the angle of elevation to be 300. Find the height of the tree.
a) 10(√3 + 1)m
b) 15√3m
c) 200(√3 + 1)m
d) 10(√3 - 1)m
Q.3. From the top of a building 60m high, the angle of elevation and depression of the top and the foot of another building are α and β respectively. Find the height of the second building.
a) 60(1+ tan α tanβ)
b) 60(1+ cot α tanβ)
c) 60(1+ tan α cotβ)
d) 60(1- tan αcotβ)
Q.4.From the top of a tower 75m high, the angles of depression of the top and bottom of a pole standing on the same plane as the tower are observed to be 300 and 450 respectively. Find the height of the pole.
a) 30.4m
b) 35.9m
c) 28.6m
d) 31.7m
Q.5.A 10 m long flagstaff is fixed on the top of a tower on the horizontal plane. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are 600 and 450 respectively. Find the height of the tower.
a) 5(√3 + 1)m
b) 5(√3 + 3)m
c) 10(√3 - 1)m
d) 10(√3 + 1)m
Q6.The angles of elevation of the top of a tower from two points on the same side of the tower are α and β (α >β). If the distance between the two points is 40m, find the height of the tower.
a) 40cotαcotβ/(tanα + tanβ)
b) 40cotαtanβ/(tanα - tanβ)
c) 40tanαtanβ/(tanα - tanβ)
d) 40tanαtanβ/(tanα + tanβ)
Q.7.The angle of elevation of the top of a tower from point A on the ground is 300. On moving a distance of 40m towards the foot of the tower, the angle of elevation increases to 450. Find the height of the tower.
a) 48.6m
b) 42.84m
c) 54.64m
d) 58.76m
Q8.An aeroplane, when 4000m high from the ground, pass vertically above another aeroplane at an instance when the angles of elevation of the two aeroplanes from the same point on the ground are 600 and 300 respectively. Find the vertical distance between the two aero planes.
a) 8000/3m
b) 8000/7m
c) 6000/7m
d) 1200m
Q9.A car is moving at uniform speed towards a tower. It takes 15 minutes for the angle of depression from the top of tower to the car to change from 300 to 600. What time after this, the car will reach the base of the tower?
a) 6 min
b) 6.5 min
c) 7 min
d) 7.5 min
Q10.A man is watching from the top of a tower, a boat speeding away from the tower. The angle of depression from the top of the tower to the boat is 600 when the boat is 80m from the tower. After 10 seconds, the angle of depression becomes 300. What is the speed of the boat? (Assume that the boat is running in still water).
a) 20 m/sec
b) 10 m/sec
c) 16 m/sec
d) 18 m/sec