Class 10 - Mathematics

Some applications of Trigonometry Online MCQ Test

Olympiad Level MCQs Also Included

Set-1

1. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower

(A) 20`(\sqrt3-1)`m
(B) `20\sqrt3` m
(C) 20 m
(D) 40 m

2. From the figure, find the value of `\frac{tanθ}{tanф}` and it is given that 'D' be the mid point of BC.

(A) `\frac{3}{4}`
(B) `\frac{1}{2}`
(C) `\frac{1}{\sqrt2}`
(D) `\frac{4}{7}`

3. The angles of elevation of the top of a tower, as seen from two points A and B situated in the same line and at distance x and y respectively. from the foot of the tower are complementary. Find the height of the tower.

(A) `\sqrt{x+y}`
(B) `\sqrt{xy}`
(C) `xy`
(D) `\sqrt{x} + \sqrt{y}`

4. A 15m long ladder placed vertically along a wall broke in such a way that its top touches the ground making an angle of 60° with it. At what height from the ground did the ladder break?

(A) 7.34m
(B) 8m
(C) 9.46m
(D) 6.96m

5. A tree 6 m tall casts a 4cm long shadow. At the same time, a flag pole casts a shadow 50m long. How long is the flag pole?

(A) 75m
(B) 100m
(C) 150m
(D) 50m

6. The height of a tower is h and the angle of elevation of the top of the tower is α. On moving a distance `\frac{h}{2}` towards the tower, the angle of elevation becomes β. What is the value of `cotα-cotβ`?

(A) `\frac{1}{2}`
(B) `\frac{2}{3}`
(C) 1
(D) 2

7. A bridge across a river makes an angle of 45° with the river bank. If the length of the bridge across the river is 150 m, width of the river is

(A) `75\sqrt{2}`m
(B) 150m
(C) `\frac{75}{\sqrt{2}}`m
(D) 75m

8. A professor standing on one end of a football field observes the elevation of the top of a flood light tower at an angle of α. He then walks a distance equal to twice the height of the tower and finds that the elevation of the top is now at an angle of 90°. What is the value of tanα ?

(A) `1-\sqrt{2}`
(B) `\sqrt{2}-1`
(C) `\sqrt{2}`
(D) 1

9. An electrician has a repair an electric fault on a pole of height 5 em. He has to reach a point 1.3 m below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use which, when inclined at an angle of 60° to the horizontal, would enable him 10 reach the required position? Also, how far from the foot of the pole should he place the foot of the ladder?

(A) 4.28m, 2.14m
(B) 4.28m, 2.83m
(C) 4.67m, 2.14m
(D) 3.67m, 2.14m

10. An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the distance between the two planes at that instant.

(A) 3920 m
(B) 6250 m
(C) 5125 m
(D) 4444 m