Question 11
Two ships are there in the sea on either side of a light house in such a way that the ships and the light house are in the same straight line. The angles of depression of two ship as observed from the top of the light house are 60° and 45°. If the height of the light house is 200 m, find the distance between the two ships
Solution
315.33 m
Question 12
Two poles of equal heights are standing opposite to each other on either side of the road, which is 100 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles.
Solution
43.25 m
Question 13
A man standing on the deck of a ship, which is 10 m above water level, observes the angle of
elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find
the distance of the hill from the ship and the height of the hill.
Solution
So distance of hill from ship =10√3 m and the height of the hill = 40m
Question 14
The angles of elevation of the top of a rock from the top and foot of 100 m high tower are respectively 30° and 45°. Find the height of the rock .
Solution
50(3 + √3)
Question 15
The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45° and 30°. If the ships are 200 m apart, find the height of the light house.
Solution
273 m
Question 16
From the top of a 60 m high building, the angles of depression of the top and the bottom of a tower are 45°and60°respectively. Find the height of the tower.
Solution
25.4 m
Question 17
The angle of elevation of a aeroplane from a point A on the ground is 60°. After
a flight of 30 seconds, the angle of elevation changes to 30°. If the aeroplane is
flying at a constant height of 3600√3 metres then find the speed of the
aeroplane
Solution
Distance covered in 30 seconds = y – x = (10800 – 3600) m = 7200 m
Speed of the plane = 240 X 18/5km/h = 864 km/h
Question 18
On a straight line passing through the foot of a tower, two points C and D are
at distances of 4 m and 12 m from the foot respectively. If the angles of
elevation from C and D of the top of the tower are complementary and angle
of elevation at C is 60° then find the height of the tower
Solution
h = 4√3 m
Question 19
Two men on either side of a 75 m high building and in line with base of building observe the angle of elevation of the top of the building as 30° and 60°. Find the distance between two men. (Use √3 = 1.73)
Solution
Distance between two men = 173 m
Question 20
A boy 1.7 m tall is standing on a horizontal ground, 50 m away from a building. The angle of elevation of the top of the building from his eye is 60°. Calculate the height of the building. (Take √3 = 1.73)
Solution
= 88.2 m
SELF ASSESSMENT
Q1. Popeye is standing on the deck of a ship which is 25 m above the water level.As seen from
the deck, the angle of elevation of the top of a hill is 60° and the angle of depression of the
bottom of the hill is 30°.
I) Draw a diagram for the above situation.
ii)Find the height of the hill
Q2. A light house is such that its angle of elevation from a point due north is 𝜃 and from a point
due west is 𝜃.Also, the distance between the points is ‘l’.Find the height of the light house.
Q3. A guard, stationed at the top of a 300 m tower, observed an unidentified boat
coming towards it. A clinometer or inclinometer is an instrument used for
measuring angles or slopes. The guard used the clinometer to measure the
angle of depression of the boat coming towards the lighthouse and found it to
be 30°
(i) Make a labelled figure on the basis of the given information and
calculate the distance of the boat from the foot of the observation
tower.
(ii) After 10 minutes, the guard observed that the boat was approaching
the tower and its distance from tower is reduced by 300 ( √3 – 1 ) m.
He immediately raised the alarm. What was the new angle of
depression of the boat from the top of the observation tower?
Q4. On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 12 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary and angle of elevation at C is 60° then find the height of the tower.
Q5. A boy 1.7 m tall is standing on a horizontal ground, 50 m away from a building. The angle of
elevation of the top of the building from his eye is 60°. Calculate the height of the building.
(Take √3 = 1.73)
Q6. The two palm trees are of equal heights and are standing opposite to each other on either side
of the river, which is 80 m wide. From a point O between them on the river the angles of
elevation of the top of the trees are 60° and 30°, respectively. Find the height of the trees and
the distances of the point O from the trees. (use √3 = 1.73)
Q7. Two men on either side of a 75 m high building and in line with base of building observe the
angles of elevation of the top of the building as 30° and 60°. Find the distance between the
two men. (Use √3 = 1.73)
Q8. The length of a string between a kite and a point on the ground is 90 m. If the
string makes an angle θ with the ground level such that tan θ= 15/8, how high
is the kite? Assume that there is no slack in the string .
Q9. The angle of elevation of the top of a vertical tower from a point on the ground
is 60°. From another point 10m vertically above the first, it’s angle of elevation
is 45°. Find the height of the tower
