Trigonometry - Tamil Nadu Board STD 10 MATHS Questions - Vidyadip

Question types

Trigonometry question types

68 questions across 3 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

68

Questions

3

Question groups

5

Question types

[2 Mark Questions]

[5 Mark Questions]

Choose the most appropriate answer from the given alternatives and write the option code and the corresponding answer.

Sample Questions

Trigonometry questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1[2 Mark Questions]2 Marks

A building and a statue are in opposite side of a street from each other 35 m apart. From a point on the roof of building the angle of elevation of the top of statue is 24° and the angle of depression of base of the statue is 34°. Find the height of the statue. (tan 24° = 0.4452, tan 34° = 0.6745)

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Q 2[2 Mark Questions]2 Marks

A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away. How far is C to the East of B?
(sin 55° = 0.8192, cos 55° = 0.5736, sin 42° = 0.6691, cos 42° = 0.7431)

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Q 3[2 Mark Questions]2 Marks

A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away. How far is B to the North of A?
(sin 55° = 0.8192, cos 55° = 0.5736, sin 42° = 0.6691, cos 42° = 0.7431)

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Q 4[2 Mark Questions]2 Marks

A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away. How far is B to the West of A?
(sin 55° = 0.8192, cos 55° = 0.5736, sin 42° = 0.6691, cos 42° = 0.7431)

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Q 5[2 Mark Questions]2 Marks

A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away. How far is C to the North of B?
(sin 55° = 0.8192, cos 55° = 0.5736, sin 42° = 0.6691, cos 42° = 0.7431)

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Q 6[5 Mark Questions]5 Marks

Two ships are sailing in the sea on either side of the lighthouse. The angles of depression of two ships as observed from the top of the lighthouse are $60^{\circ}$ and $45^{\circ}$ respectively. If the distance between the ships is $200\left[\frac{\sqrt{3}+1}{\sqrt{3}}\right]$ metres, find the height of the lighthouse.

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Q 7[5 Mark Questions]5 Marks

An aeroplane is flying parallel to the Earth’s surface at a speed of 175 m/sec and at a height of 600 m. The angle of elevation of the aeroplane from a point on the Earth’s surface is 37°. After what period of time does the angle of elevation increase to 53°? (tan 53° = 1.3270, tan 37° = 0.7536)

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Q 8[5 Mark Questions]5 Marks

A bird is sitting on the top of a $80 m$ high tree. From a point on the ground, the angle of elevation of the bird is $45^{\circ}$. The bird flies away horizontally in such away that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is $30^{\circ}$. Determine the speed at which the bird flies $(\sqrt{3}=1.732)$

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Q 9[5 Mark Questions]5 Marks

The angles of elevation and depression of the top and bottom of a lamp post from the top of a 66 m high apartment are 60° and 30° respectively. Find the height of the lamp post

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Q 10[5 Mark Questions]5 Marks

A lift in a building of height 90 feet with transparent glass walls is descending from the top of the building. At the top of the building, the angle of depression to a fountain in the garden is $60^{\circ}$. Two minutes later, the angle of depression reduces to $30^{\circ}$. If the fountain is $30 \sqrt{3}$ feet from the entrance of the lift, find the speed of the lift which is descending.

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Q 11Choose the most appropriate answer from the given alternatives and write the option code and the corresponding answer.1 Mark

$a \cot \theta+b \operatorname{cosec} \theta=p$ and $b \cot \theta+a \operatorname{cosec} \theta=q$ then $p^2-q^2$ is equal to . ……………..

A
$a^2-b^2 $
✓
$ b^2-a^2 $
C
$ a^2+b^2 $
D
b – a

Answer: B.

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Q 12Choose the most appropriate answer from the given alternatives and write the option code and the corresponding answer.1 Mark

(1 + tan θ + sec θ) (1 + cot θ – cosec θ) is equal to …………..

A
0
B
1
✓
2
D
− 1

Answer: C.

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Q 13Choose the most appropriate answer from the given alternatives and write the option code and the corresponding answer.1 Mark

If $x=a \tan \theta$ and $y=b \sec \theta$ then ………..

✓
$\frac{y^2}{ b ^2}-\frac{x^2}{ a ^2}=1$
B
$\frac{x^2}{ a ^2}-\frac{y^2}{ b ^2}=1$
C
$\frac{x^2}{ a ^2}+\frac{y^2}{ b ^2}=1$
D
$\frac{x^2}{ a ^2}-\frac{y^2}{ b ^2}=0$

Answer: A.

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Q 14Choose the most appropriate answer from the given alternatives and write the option code and the corresponding answer.1 Mark

If $\sin \theta=\cos \theta$, then $2 \tan ^2 \theta+\sin ^2 \theta-1$ is equal to ………………

A
$\frac{-3}{2}$
✓
$\frac{3}{2}$
C
$\frac{2}{3}$
D
$\frac{-2}{3}$

Answer: B.

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Q 15Choose the most appropriate answer from the given alternatives and write the option code and the corresponding answer.1 Mark

If $5 x=\sec \theta$ and $\frac{5}{x}=\tan \theta$, then $x^2-\frac{1}{x^2}$ is equal to ………….

A
25
B
$\frac{1}{25}$
C
5
✓
1

Answer: D.

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