Class 10 Practice – Level 3 – Set 1 – Trigonometry

Total questions: 15

The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be 60° and 30°, respectively. What is the height of the balloon above the ground?

Topic: Heights and Distances

10 m

8 m

12 m

14 m

None

A window of a house is hm above the ground. Form the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. What will be the height of the other house in m?

Topic: Heights and Distances

h(1+tanα⋅cotβ)

h(1+cos α⋅cotβ)

h(1+sin α⋅cotβ)

h(1+tanα⋅sinβ)

None

The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the other tower respectively.

Topic: Heights and Distances

15√2 m, 15 m

15√3 m, 20 m

10√3 m, 30 m

10√3 m, 10 m

None

The shadow of a tower standing on a level plane is found to be 50 m longer when Sun's elevation is 30° than when it is 60°. Find the height of the tower.

Topic: Heights and Distances

45√3 m

25√3 m

65√3 m

35√3 m

None

The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Find the height of the tower.

Topic: Heights and Distances

√st

s√t

√2st

None

If sinθ+2cosθ=1, then 2sinθ−cosθ will be equal to:

Topic: Trigonometric Identities

None

If 1+sin² θ = 3 sinθ cosθ, then find tanθ.

Topic: Trigonometric Identities and Equations

$\displaystyle \dfrac{1}{2}$

0.5

All of the above

None

An observer 1.5 m tall is 20.5 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.

Topic: Angle of Elevation

45°

35°

25°

15°

None

A ladder 15 m long just reaches the top of a vertical wall. If the ladders makes an angle of 60° with the wall, then the height of the wall will be:

Topic: Heights and Distances

$\displaystyle \dfrac{{30}}{2}$

$\displaystyle \dfrac{{45}}{2}$

$\displaystyle \dfrac{{15}}{2}$

$\displaystyle \dfrac{{20}}{2}$

None

10.

Find out the % increase in the height of a tower and the distance of the point of observation from its foot, that will not change the angle of elevation of its top.

Topic: Angle of Elevation

10%

20%

15%

12%

None

11.

The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will be:

Topic: Effect of Height on Angle of Elevation

30°

60°

<60°

<30°

None

12.

If a man standing on a plat form 3 m above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection. Is the statement true?

Topic: Reflection and Elevation

True

False

Cannot be predicted

Incomplete information

None

13.

Solve : sin² 25°+ sin²65° +√3 (tan5° tan15° tan30° tan75° tan85°).

Topic: Trigonometric Identities

None

14.

In the following figure, ABCD is a rectangle in which the segments AP and AQ are drawn as shown. Find the length of (AP+AQ).

Topic: Geometry and Trigonometry

160 cm

120 cm

180 cm

150 cm

None

15.

If cos 9A = sin A and 9A < 90°, then the value of tan 5A is:

Topic: Trigonometric Equation

√3

$ \displaystyle \dfrac{1}{√3}$

None

1 out of 15

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Class 10 Practice – Level 3 – Set 1 – Trigonometry

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