Class 10 Practice – Level 3 – Set 2 – Some Application of Trigonometry

Total questions: 15

The angle of elevation of the top of an unifinished tower at a distance of 75 m from its base is 30°. How much higher must be tower be raised so that the angle of elevation of its top at the same point may be 60°?

Topic: Properties of Width

56.4 m

44.5 m

56.6 m

86.6 m

None

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6 m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 60°. Find the height of the tower. [use √3=1.732]

Topic: Properties of Height

4 m

3 m

60 m

10 m

None

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 30 meters away from the bank, he finds the angle of elevation to be 30°. Find the width of the river.(in meters) [Take √3 =1.732.]

Topic: Width Using Angles of Elevation

60 m

15 m

20 m

30 m

None

A vertical tower of height 20 m stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angle of elevation of the bottom and top of the flag staff are 45° and 60° respectively. Then the value of h is:

Topic: Properties of Height

20(√3-1) m

90(√3-1) m

40(√3-1) m

30(√3-1) m

None

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60°, and the angle of depression of its foot is 45°. Find the height of the tower. Given that √3=1.732.

Topic: Properties of Height

15.254 m

15.325 m

78.326 m

19.124 m

None

A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle of elevation of the top of the light house from 60° to 30°. Find the speed of the boat in meters per minute. [ Use √3=1.732]

Topic: Properties of Distance

57.73 m / min

25.36 m / min

12.25 m / min

63.12 m / min

None

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 6 m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are 30° and 45° respectively. Find the height of the tower. (Take √3 =1.73 )

Topic: Properties of Height

6.12 m

32.2 m

8.19 m

8.23 m

None

The ratio of the length of a vertical rod and the length of its shadow is 1:√3. Find the angle of elevation of the sun at that moment.

Topic: Properties of Length

30°

60°

90°

50°

None

The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°, if the tower is 60 m high, then the height of the building will be:

Topic: Height using Trigonometry

20 m

50 m

60 m

40 m

None

10.

The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle 30° with the horizontal, then the length of the wire is:

Topic: Properties of Length

26 m

10 m

12 m

14 m

None

11.

Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point P between them on the road, the angle of elevation of the top of one pole is 60° and the angle of depression from the top of another pole at P is 30°. Then the height of each pole and distance of the point P from the poles is:

Topic: Heights and Distances

h= 20√3 m, d= 60 m, 20 m

h= 10√3 m, d= 80 m, 20 m

h= 20√2 m, d= 60 m, 40 m

h= 10)√2 m, d= 100 m, 40 m

None

12.

A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a second point, h meter above first, the depression of the foot of the tower is 60°, the horizontal distance of the tower from the point is-

Topic: Properties of Distance

$\displaystyle \dfrac{h}{3}\ $

$\displaystyle \dfrac{h}{2}\ $

√3h

None

13.

Each side of an equilateral triangle subtends an angle of 60° at the top of a tower 'h' m high located at the center of the triangle. If a is the length of each side of the triangle, then:

Topic: Trigonometric Application in an Equilateral Triangle

2a² = 3 h²

3a² = 2 h²

a² = 3 h²

3a² = h²

None

14.

The angle of elevation of a cloud from a point situated at a metre height from a lake is a and the angle of depression of its reflection is b. Height of the cloud is:

Topic: Height using Trigonometry

$\displaystyle \dfrac{{a\sin \left( {\alpha +\beta } \right)}}{{\sin \left( {\beta -\alpha } \right)}} m$

$\displaystyle \dfrac{{a\cos \left( {\alpha +\beta } \right)}}{{\cos \left( {\beta -\alpha } \right)}} m$

$\displaystyle \dfrac{{a\sin \left( {\alpha +\beta } \right)}}{{\cos \left( {\beta -\alpha } \right)}} m$

$\displaystyle \dfrac{{a\cos\left( {\alpha +\beta } \right)}}{{\sin\left( {\beta -\alpha} \right)}} m$

None

15.

From vertically situated aeroplane to the straight horizontal road, the angle of depression of two consecutive km stones are a and b. If an aeroplane is in vertical plane in between two stones, then the height of the aeroplane from the road (in kilometers) will be:

Topic: Height using Angles of Depression

$\displaystyle \dfrac{{\tan \alpha tan\beta }}{{\tan \alpha +tan\beta }}$

$\displaystyle \dfrac{{\sin \alpha tan\beta }}{{\sin \alpha +tan\beta }}$

$\displaystyle \dfrac{{\cos \alpha tan\beta }}{{\cos \alpha +tan\beta }}$

$\displaystyle \dfrac{{cosec \alpha tan\beta }}{{\sec \alpha +tan\beta }}$

None

1 out of 15

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Class 10 Practice – Level 3 – Set 2 – Some Application of Trigonometry

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