This set of Mathematics Question Papers for Class 10 focuses on “Trigonometric Ratios – 3”.

1. If sin A = \(\frac {3}{5}\), then find tan A.

a) \(\frac {3}{4}\)

b) \(\frac {3}{5}\)

c) \(\frac {5}{3}\)

d) \(\frac {4}{3}\)

View Answer

Explanation: Sin A = \(\frac {Opposite \, side}{Hypotenuse} = \frac {3}{5}\)

From Pythagoras theorem, (Hypotenuse)

^{2}= (Opposite side)

^{2}+ (Adjacent side)

^{2}

5

^{2}= 3

^{2}+ (Adjacent side)

^{2}

(Adjacent side)

^{2}= 5

^{2}– 3

^{2}

Adjacent side = √16 = 4

Tan A = \(\frac {Opposite \, side}{Adjacent \, side} = \frac {3}{4}\)

2. \(\frac {Cos A}{Sin A}\) = ______

a) Tan A

b) Sin A

c) Cot A

d) Sec A

View Answer

Explanation: Sin A = \(\frac {Length \, of \, the \, opposite \, side}{Length \, of \, the \, hypotenuse}\), Cos A = \(\frac {Length \, of \, the \, adjacent \, side}{Length \, of \, the \, hypotenuse}\)

\(\frac {Cos A}{Sin A} = \frac {Length \, of \, the \, adjacent \, side}{Length \, of \, the \, opposite \, side}\)

= Cot A

3. If sin B = \(\frac {3}{5}\), then find sec B.

a) \(\frac {3}{4}\)

b) \(\frac {4}{5}\)

c) \(\frac {5}{4}\)

d) \(\frac {5}{3}\)

View Answer

Explanation: Sin B = \(\frac {Opposite \, side}{Hypotenuse} = \frac {3}{5}\)

From Pythagoras theorem, (Hypotenuse)

^{2}= (Opposite side)

^{2}+ (Adjacent side)

^{2}

5

^{2}= 3

^{2}+ (Adjacent side)

^{2}

(Adjacent side)

^{2}= 5

^{2}– 3

^{2}

Adjacent side = √16 = 4

Sec B = \(\frac {Hypotenuse}{Adjacent \, side} = \frac {5}{4}\)

4. What is the value of cos^{2}θ – sin^{2}θ if the length of the opposite side is 20 units and the length of the hypotenuse is 29 units?

a) \(\frac {- 41}{841}\)

b) \(\frac {- 41}{840}\)

c) \(\frac {41}{841}\)

d) \(\frac {41}{840}\)

View Answer

Explanation: From Pythagoras theorem, (Hypotenuse)

^{2}= (Opposite side)

^{2}+ (Adjacent side)

^{2}

(Adjacent side)

^{2}= (Hypotenuse)

^{2}– (Opposite side)

^{2}

Adjacent side = √441 = 21

Cosθ = \(\frac {Length \, of \, the \, adjacent \, side}{Length \, of \, the \, hypotenuse} = \frac {21}{29}\), Sinθ = \(\frac {Length \, of \, the \, opposite \, side}{Length \, of \, the \, hypotenuse} = \frac {20}{29} \)

cos

^{2}θ – sin

^{2}θ = (\(\frac {21}{29}\))

^{2}+ (\(\frac {20}{29} \))

^{2}

= \(\frac {- 41}{841}\)

5. If the length of the side opposite to angle A is 15 units and the length of the hypotenuse is 17 units then the length of the side adjacent to angle A is _____

a) 8 units

b) 7 units

c) 4 units

d) 5 units

View Answer

Explanation: From Pythagoras theorem, (Hypotenuse)

^{2}= (Opposite side)

^{2}+ (Adjacent side)

^{2}

(Adjacent side)

^{2}= (Hypotenuse)

^{2}– (Opposite side)

^{2}

Adjacent side = \(\sqrt {289 – 225}\) = 8 units

6. The meaning of the word trigonometry is three angles measure.

a) True

b) False

View Answer

Explanation: The word trigonometry is from the language Greek where ‘Tri’ means three and ‘Goria’ means ‘angle’ and ‘Metron’ means measure which gives the meaning as three angles measure.

7. Trigonometry is also applicable to obtuse angles triangles.

a) True

b) False

View Answer

Explanation: Trigonometry is only applicable to right – angled triangles whose angle is 90° between two sides of a triangle and it gives the relation between the length of sides and angles of a right – angled triangle.

8. If the length of the opposite side is 20 units and the length of the hypotenuse is 29 units then find cosec A?

a) \(\frac {20}{29}\)

b) \(\frac {29}{21}\)

c) \(\frac {21}{20}\)

d) \(\frac {29}{20}\)

View Answer

Explanation: Cosec A = \(\frac {Length \, of \, the \, hypotenuse}{Length \, of \, the \, opposite \, side}\)

= \(\frac {29}{20}\)

9. If tan A = \(\frac {89}{17}\), then cot A is _____

a) \(\frac {89}{17}\)

b) \(\frac {89}{16}\)

c) \(\frac {17}{89}\)

d) \(\frac {16}{89}\)

View Answer

Explanation: Tan A and cot A are reciprocal ratios and cot is inverse of tan.

Tan A = \(\frac {1}{Cot A} = \frac {1}{89/17}\)

= \(\frac {17}{89}\)

10. If cos C = \(\frac {8}{17}\) and sec C = \(\frac {17}{8}\), then 1 is the product of cos C and sec C.

a) False

b) True

View Answer

Explanation: Cos and sine are reciprocal trigonometric ratios. These two ratios are inverse to each other.

Cos C = \(\frac {1}{Sec \, C}\)

(Cos C)(Sec C) = 1

\((\frac {8}{17}) (\frac {17}{8})\) = 1

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