Applications Of Trigonometry(10th Grade > Mathematics ) Questions and answers for exam Preparation

10th Grade > Mathematics

APPLICATIONS OF TRIGONOMETRY MCQs

Total Questions : 58 | Page 2 of 6 pages

Question 11. A kite is attached to a string of length 20

\sqrt{3}

m is tied to a pole on the level ground. If the string of the kite makes an angle of elevation of

60^{\circ}

with the ground, then the kite is flying at a height of 20 m.

True
False

Discuss Question

Answer: Option B. -> False
:
B

A kite Is Attached To A String Of Length 20√3m Is Tied To...

s i n ∠ A C B = \frac{A B}{A C} \Rightarrow s i n 60^{\circ} = \frac{A B}{A C} \Rightarrow A B = A C \times s i n 60^{\circ} = 20 \sqrt{3} \times \frac{\sqrt{3}}{2} ∴ Height of the kite is 30 m .

Question 12. The tops of two poles of height 14 m and 20 m are connected by a wire which makes an angle of 30° with the horizontal. The length of the wire is _____m.

Discuss Question

Answer: Option D. -> 12m
:
D

The Tops Of Two Poles Of Height 14 M And 20 M Are Connected ...

In triangle ABC,
BC = y = 20-14 = 6m;
Let AB =

x

\Rightarrow

Sin

30^{\circ}

\frac{B C}{A B}

\Rightarrow

\frac{1}{2}

\frac{6}{x}

\Rightarrow

x

= 12
Thus, the length of the string is 12 m.

Question 13. Two towers A and B are standing at some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be

30^{\circ}

. From the top of tower B, the angle of depression of the foot of tower A is found to be

60^{\circ}

. If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is _____ m

h2m
h3m
√3hm
h√3m

Discuss Question

Answer: Option B. -> h3m
:
B

Two towers A And B Are Standing At Some Distance Apart. Fro...

Let the height of tower A be = AB = H.
And the height of tower B = CD = h
In triangle ABC
tan

30^{\circ}

\frac{A B}{A C}

\frac{H}{A C}

...... (1)
In triangle ADC
tan

60^{\circ}

\frac{C D}{A C}

\frac{h}{A C}

...... (2)
Dividing(1) by (2) we get,

\frac{t a n 30^{\circ}}{t a n 60^{\circ}}

\frac{H}{h}

\frac{h}{3}

Question 14. A kite is flying on a string of 40 m. 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^{\circ}

. Find the height at which the kite is flying.

10 m
30 m
20 m
40 m

Discuss Question

Answer: Option C. -> 20 m
:
C
The situation can be represented by the figure below:

A Kite Is Flying On A String Of 40 M. The String Attached To...

AB is the height at which the kite is flying.

s i n (∠ A C B) = \frac{A B}{A C} \Rightarrow s i n 30^{\circ} = \frac{A B}{A C} \Rightarrow \frac{1}{2} \times 40 = A B \Rightarrow A B = 20 m

Question 15. A Technician has to repair a light on a pole of height 10 m. She needs to reach a point 2 m below the top of the pole to undertake the repair work. The length of the ramp that she should use which, when inclined at an angle of

30^{\circ}

to the horizontal, would enable her to reach the required position, is
___ m
(You may take

\sqrt{3}

= 1.73)

Discuss Question

A Technician Has To Repair A Light On A Pole Of Height 10 M....

Let BD be the height of the pole. And A is the point where she has to do the repair work.
So, distance of the point she should reach = AB = 10 - 2 = 8 m
In the given right-angled triangle,

S i n 30^{\circ} = \frac{A B}{A C}

\Rightarrow \frac{1}{2} = \frac{8}{A C}

Hence, height of the Ramp AC =2

\times

8 = 16m

Question 16. The angles of depression of two objects from the top of a 100 m hill lying to its east are found to be

45^{\circ} a n d 30^{\circ}

. Find the distance between the two objects. (Take

\sqrt{3} = 1.732

)

73.2 metres
107.5 meters
150 metres
200 metres

Discuss Question

Answer: Option A. -> 73.2 metres
:
A
Let C and D be the objects and CD be the distance between the objects.

The Angles Of Depression Of Two Objects From The Top Of A 10...

Δ A B C

t a n 45^{\circ}

\frac{A B}{A C}

= 1

A B = A C = 100 m

Δ A B D

t a n 30^{\circ}

\frac{A B}{A D}

A D \times \frac{1}{\sqrt{3}} = 100

A D = 100 \times \sqrt{3} = 173.2 m

C D = A D - A C = 173.2 - 100 = 73.2 m e t r e s

Question 17. Two ships are on either side of a 100 m lighthouse. The angles of elevation from the two ships to the top of the lighthouse are 30° and 45°. Find the distance between the ships.

300 m
173 m
273 m
200 m

Discuss Question

Answer: Option C. -> 273 m
:
C

Two Ships Are On Either Side Of A 100 M Lighthouse. The Angl...

Let, BD be the lighthouse and A and C be the positions of the ships.
Then, BD = 100 m,

∠

BAD = 30

^{\circ}

∠

BCD = 45

^{\circ}

t a n 30^{\circ} = \frac{B D}{B A} \Rightarrow \frac{1}{\sqrt{3}} = \frac{100}{B A} \Rightarrow B A = 100 \sqrt{3} t a n 45^{\circ} = \frac{B D}{B C} \Rightarrow 1 = \frac{100}{B C} \Rightarrow B C = 100

Distance between the two ships

= A C = B A + B C = 100 \sqrt{3} + 100 = 100 (\sqrt{3} + 1) = 100 (1.73 + 1) = 100 \times 2.73 = 273 m

Question 18. A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 cm long. Determine the height of the tower?