# Free Applications of Trigonometry 01 Practice Test - 10th Grade

State whether the given statement is true or false:

The angle of depression is the angle between the line of sight of an observer below his horizontal line of sight.

A.

True

B.

False

#### SOLUTION

Solution : A The angle of depression is the angle between the line of sight of an observer below his horizontal line of sight.

State whether the given statement is true or false:

The angle of elevation is the angle between the line of sight of an observer below his horizontal line of sight.

A.

True

B.

False

#### SOLUTION

Solution : B

The angle of elevation is the angle between the line of sight of an observer above his horizontal line of sight. A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The height of the pole, if the angle made by the rope with the ground level is 30

___

m.

#### SOLUTION

Solution : The figure above represents the given situation.
In the given figure,
sin30=ABACAB=sin30×AC           =AC2=302=15m.

A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle made by the rope with the ground level is 30.

A.

5 m

B.

153 m

C.

18 m

D.

20 m

#### SOLUTION

Solution : B The figure above represents the given situation.
From the given firgure,
cos30=BCACBC=AC×cos30=3032
=153m

A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of 30 to the ground. What should be the length of the slide?

A.

3 m

B.

1.5 m

C.

2 m

D.

4 m

#### SOLUTION

Solution : D

The given situation can be represented by the figure below In right-angled triangle ABC,
sinABC=ACAB=12sin30=2ABAB=212AB=4mLength of the slide is 4m.

A contractor plans to install two slides for the children to play in a park for elder children. She wants to have a steep slide at a height of 6 m, and inclined at an angle of 60 to the ground. What should be the length of the slide (in m)?

A.

33 m

B.

5 m

C.

43 m

D.

6 m

#### SOLUTION

Solution : C The above figure represents the given situation.
In the given right-agled triangle,
sin(ACB)=ABACsin60=6ACAC=632=123=43 mlength of slide=43 m

A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60. Find the length of the string, assuming that there is no slack in the string.

A.

203 m

B.

30 m

C.

303 m

D.

60 m

#### SOLUTION

Solution : A

The situation can be represented by the figure below: In the given right-angled triangle:
sin(ACB)=ABAC
sin60=ABAC
AC=ABsin60=3032=603=203
Length of the string is 203 m.

A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 30. Find the length of the string(in meters), assuming that there is no slack in the string.

A.

60 m

B.

40 m

C.

30 m

D.

203 m

#### SOLUTION

Solution : A

The given situation can be represented by the figure below In the given right-angled triangle,
sin30=ABACAC=ABsin30=3012=60m
Therefore length of the string is 60 m.

A 1.8 m tall man is standing at some distance from a 31.8 m tall building. The angle of elevation from his eyes to the top of the building increases from 30 to 60 as he walks towards the building. Find the distance he walked towards the building.

A.

30 m

B.

203 m

C.

20 m

D.

303 m

#### SOLUTION

Solution : B The situation can be represented by the figure above,
tan(ACB)=ABBCtan60=30BCBC=30tan60=103mtan(ADB)=ABBDtan30=30BDBD=3013=303mDistance walked=DC=BDBC=303103=203m

A 1.8 m tall man is standing at some distance from a building. The angle of elevation from his eyes to the top of the building increases from 30 to 60 as he walks 20 m towards the building. Find the height of the building (in m).

A.

10 m

B.

203 m

C.

20 m

D.

(103 + 1.8) m

#### SOLUTION

Solution : D The situation can be represented by the figure above.
tan(ACB)=ABBCBC=ABtan60.....(1)tan(ADB)=ABBDtan30=ABBC+CDBC+CD=ABtan30.....(2) on subtracting equation(1) from (2)CD=ABtan30ABtan60AB=103
Hence, the height of the building is
= AB + BG = (103+1.8)m.