SOME APPLICATIONS OF TRIGONOMETRY Test-04

This is SOME APPLICATIONS OF TRIGONOMETRY Test-04 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

An electric pole is tied from the top to a point (some distance away from the base) on the ground using a string. The ratio of the height of pole to the string is $\sqrt 3 $ : 2, then the angle of elevation of the top from the point on the ground is

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

A circus artist is climbing a long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The ratio of the height of the pole to the length of the string is 1 :$\sqrt 2 $. The angle made by the rope with the ground level is

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

Two men are on opposite sides of a tower. They observe the angles of elevation of the top of the tower as $30^\circ $ and $45^\circ $ respectively. If the height of the tower is 100m, then the distance between them is

A
$100(1 - \sqrt 3 )m$
B
$100(\sqrt 3 - 1)m$
C
$100(\sqrt 3 + 1)m$
Correct
D
none of these

Two men are on the same side of a tower. They observe the angles of elevation of the top of the tower as $30^\circ $ and $45^\circ $ respectively. If the height of the tower is 100m, then the distance between them is

A
none of these.
B
$100(\sqrt 3 + 1)m$
C
$100(\sqrt 3 - 1)m$
Correct
D
$100(1 - \sqrt 3 )m$

A ladder 12m long just reaches the top of a vertical wall. If the ladder makes an angle of 45° with the wall, then the height of the wall is

A
$12\sqrt 2 m$
B
6m
C
12m
D
$6\sqrt 2 m$
Correct

A pole of height 60m has a shadow of length 20$\sqrt 3 $m at a particular instant of time. The angle of elevation of the sun at this point of time

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

In a right DABC, AC is the hypotenuse of length 10cm. If $\angle A$ = 30°, then the area of the triangle is

A
$25c{m^2}$
B
$\frac{{25}}{2}\sqrt 3 c{m^2}$
Correct
C
$25\sqrt 3 c{m^2}$
D
$\frac{{25}}{3}\sqrt 3 c{m^2}$

A boy is flying a kite, the string of the kite makes an angle of 30° with the ground. If the height of the kite is 18m, then the length of the string is

A
18m
B
$36\sqrt 3 m$
C
$18\sqrt 3 m$
D
36m
Correct

In a right$\Delta PQR$ , PR is the hypotenuse of length 20cm and $\angle P{\text{ }} = {\text{ }}60^\circ .$ The area of the triangle is

A
$50\sqrt 3 c{m^2}$
Correct
B
$50c{m^2}$
C
$100c{m^2}$
D
$100\sqrt 3 c{m^2}$

Two men are on opposite sides of a tower. They observe the angles of elevation of the top of the tower as $60^\circ $ and $45^\circ $ respectively. If the height of the tower is 60m, then the distance between them is

A
$20(3 - \sqrt 3 )m$
B
$20(3 + \sqrt 3 )m$
Correct
C
none of these.
D
$20(3 - \sqrt 3 )m$

In a right $\Delta XYZ$ , XZ is the hypotenuse of length 12cm and $\angle X{\text{ }} = {\text{ }}45^\circ .$ The area of the triangle is

A
$24c{m^2}$
B
$36c{m^2}$
Correct
C
$12c{m^2}$
D
$72c{m^2}$

If the length of a shadow of a tower is increasing, then the angle of elevation of the sun is

A
neither increasing nor decreasing
B
decreasing
Correct
C
none of these
D
increasing

If two trees of height ‘x’ and ‘y’ standing on the two ends of a road subtend angles of and $60^\circ $ respectively at the midpoint of the road, then the ratio of x : y is

A
1 : 3
Correct
B
3 : 1
C
1 : 2
D
1 : 1

A 1.2m tall boy stands at a distance of 2.4m from a lamp post and casts a shadow of 3.6m on the ground. The height of the lamp post is

A
4m
B
6m
C
2m
Correct
D
3m

If the angles of elevation of a tower from two points at distances ‘m’ and ‘n’ where m > n from its foot and in the same line from it are 30° and 60°, then the height of the tower is

A
$\sqrt {\frac{m}{n}} $
B
$\sqrt {mn} $
Correct
C
$\sqrt {m - n} $
D
$\sqrt {m + n} $