SOME APPLICATIONS OF TRIGONOMETRY Test

SOME APPLICATIONS OF TRIGONOMETRY

This is SOME APPLICATIONS OF TRIGONOMETRY Test-05 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

The ratio between the height and the length of the shadow of a pole is \(\sqrt 3 \) : 1, then the sun’s altitude is

A
\(75^\circ \)
B
\(30^\circ \)
C
\(60^\circ \)
Correct
D
\(45^\circ \)

A vertical stick 20cm long casts a shadow 15cm long. At the same time, a tower casts a shadow 30m long. The height of the tower is

A
15m
B
20m
C
30m
D
40m
Correct

The angle of depression and the angle of elevation from an object on the ground to an object in the air are related as

A
greater than
B
equal
Correct
C
all of these
D
less than

If the height of a tower is half the height of the flagstaff on it and the angle of elevation of the top of the tower as seen from a point on the ground is 30°., then the angle of elevation of the top of the flagstaff as seen from the same point is

A
\(60^\circ \)
Correct
B
none of these
C
\(30^\circ \)
D
\(45^\circ \)

A ramp for disabled people in a hospital must slope at not more than 30°. If the height of the ramp has to be 1m, then the length of the ramp be

A
\(\sqrt 3 \)m
Correct
B
3 m
C
2 m
D
1 m

A tower and a building standing on the ground are 20m apart. The height of the tower is 2 times the height of the building. If at the mid-point of the line joining their feet, the angular elevation of their tops are complementary, then the height of the building is

A
\(5\sqrt 2 \) m
Correct
B
\(\sqrt 3 \)m
C
\(\sqrt 2 \)m
D
\(\frac{2}{{\sqrt 2 }}\)m

If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top

A
none of these
B
decreases
C
increases
D
remains unchanged
Correct

A plane is observed to be approaching the airport. It is at a distance of 12 km from the point of observation and makes an angle of elevation of 30° there at. Its height above the ground is

A
12km
B
6km
Correct
C
none of these
D
10km

The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50m high, then the height of the hill is

A
150m
Correct
B
50\(\sqrt 3 \)m
C
100\(\sqrt 3 \)m
D
150\(\sqrt 3 \)m

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 5m. From a point on the plane the angles of elevation of the bottom and top of the flagstaff are respectively 30° and 60°. The height of the tower is

A
2m
B
2.5m
Correct
C
10m
D
5m

From the top of a building 60m high, the angles of depression of the top and the bottom of a tower are observed to be 30° and 60°. The height of the tower is

A
40m
Correct
B
50m
C
45m
D
60m

The angle of elevation of a plane from a point P on the ground is 60°. After a flight of 15 seconds , the angle of elevation changes to 30°. If the plane is flying at a constant height of 1500\(\sqrt 3 \)m, then the speed of the plane is

A
640 km/hr
B
720 km/hr
Correct
C
500 km/hr
D
800 km/hr

A tree 12m high is broken by the wind in such a way that its top touches the ground and makes an angle \(\tan 30^\circ \) with the ground. The height at which from the bottom the tree is broken by the wind is

A
9m
B
8m
C
4m
Correct
D
6m

A round balloon of radius ‘r’ subtends an angle ‘α’ at the eye of the observer while the angle of elevation of its centre is ‘β’. The height of the centre of the balloon is

A
\(r\sin \beta \cos ec\frac{\alpha }{2}\)
Correct
B
\(r\cos \beta \cos ec\frac{\alpha }{2}\)
C
\(r\sin \beta \sec \frac{\alpha }{2}\)
D
\(r\cos \beta \sec \frac{\alpha }{2}\)

_______ is an instrument for measuring the angles of elevation and depression.

A
Periscope
B
Telescope
C
Microscope
D
Theodolite
Correct