Class 10 Quiz Level 3 (Difficult) – Trigonometry

Total questions: 10

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

Deselect Answer

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

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

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

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

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

Deselect Answer

15√2 m, 15 m

15√3 m, 20 m

10√3 m, 30 m

10√3 m, 10 m

None

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

Deselect Answer

160 cm

120 cm

180 cm

150 cm

None

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

Topic: Trigonometric Identities and Equations

Deselect Answer

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

0.5

All of the above

None

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

Deselect Answer

10 m

8 m

12 m

14 m

None

Evaluate $ \displaystyle {{\left( {\dfrac{{\sin {{{49}}^{\circ }}}}{{\cos {{{41}}^{\circ }}}}} \right)}^{2}}+{{\left( {\frac{{\cos {{{41}}^{\circ }}}}{{\sin {{{49}}^{\circ }}}}} \right)}^{2}}$.

Topic: Trigonometric Identities and Simplification

Deselect Answer