Class Test – Applications of Trigonometry
Time: 1 Hour
Section A – MCQs (10 × 1 = 10 Marks)
Choose the correct option:
1. From the top of a 60 m high building, the angle of depression of a car on the road is 30°.
The horizontal distance of the car from the building is:
(a) 60√3 m
(b) 30√3 m
(c) 20√3 m
(d) 180 m
2. A man standing on the top of a 75 m tower observes the top of a building at an angle of
depression of 30° and the bottom of the building at 60°. The height of the building is:
(a) 25 m
(b) 50 m
(c) 60 m
(d) 75 m
3. If the angle of elevation of the sun changes from 30° to 60°, the length of the shadow of
a vertical pole of height h will:
(a) double
(b) become half
(c) remain the same
(d) none of these
4. A kite is flying at a height of 50 m with string inclined at 60°. The length of string is:
(a) 50 m
(b) 100 m
(c) 50√3 m
(d) 100√3 m
5. A person standing 50 m away from the foot of a tower finds the angle of elevation of the
top to be 45°. The height of the tower is:
(a) 25 m
(b) 50 m
(c) 75 m
(d) 100 m
6. A boy is standing on the bank of a river. The angle of elevation of the top of a tree
standing on the opposite bank is 60°. If the height of the tree is 20 m, then the width of
the river is:
(a) 20√3 m
(b) 10√3 m
(c) 20/√3 m
(d) none of these
7. The angle of elevation of the top of a hill from the ground at two points in a straight line
through the foot of the hill are 30° and 60°. If the hill is 100 m high, then the distance
between the two points is:
(a) 100√3 m
(b) 200√3 m
(c) 200 m
(d) 100 m
8. The angle of elevation of the top of a vertical tower is observed to be 45°. If on moving
20 m nearer the tower, the angle becomes 60°, then the height of the tower is:
(a) 10 m
(b) 20 m
(c) 30 m
(d) 40 m
9. A balloon is observed at an elevation of 30°. After ascending 100 m vertically, the angle
of elevation becomes 60°. The initial height of the balloon was:
(a) 100 m
(b) 50 m
(c) 200 m
(d) none of these
10. If the angle of elevation of a cloud from a point h meters above a lake is θ and the angle
of depression of its reflection in the lake is φ, then the height of the cloud above the lake
is:
(a) h(cotφ – cotθ)
(b) h(cotθ – cotφ)
(c) h(tanφ – tanθ)
(d) none of these
Section B – Descriptive Questions
Q1.
A 10 m long ladder is leaning against a vertical wall. The ladder makes an angle of 60° with the
ground. Find how high up the wall the ladder reaches and also the distance of the foot of the
ladder from the wall.
Q2.
From the top of a 50 m high tower, the angle of depression of the top and bottom of a vertical
pole is found to be 30° and 60°. Find the height of the pole.
Q3.
A flagstaff stands on the top of a tower. From a point on the ground, the angle of elevation of
the top and bottom of the flagstaff are 45° and 30°. If the height of the flagstaff is 10 m, find the
height of the tower.
Q4
The angle of elevation of the top of a hill at the foot of a tower is 60° and at the top of the tower
is 45°. If the tower is 30 m high, find the height of the hill.
Q5.
Two pillars of equal height stand on either side of a road, which is 80 m wide. From a point
between them on the road, the angles of elevation of the tops of the pillars are 30° and 60°.
Find the height of the pillars and the distance of the point from the two pillars.
Q6.
From the top of a lighthouse, the angles of depression of two ships on the same side of the
lighthouse are 30° and 60°. If the lighthouse is 100 m high, find the distance between the two
ships.