If sin θ =3/5 and θ is acute angle, find

If sin θ =3/5 and θ is acute angle, find

(i) cos θ

(ii) tan θ.

Answer :

Let ∆ ABC be a right angled at B

Let ∠ACB = θ

sin θ = 3/5

AB/AC = 3/5

Let AB = 3x

then AC = 5x

In right angled ∆ ABC,

Trigonometric Ratios Class 9 ICSE ML Aggarwal img 12

(5x)2 = (3x)+ BC2

⇒ BC2 = (5x)– (3x)2

⇒ BC= (2x)2

⇒ BC = 4x

(i) cos θ = Base/ Hypotenuse

= BC / AC

= 4x /5x

= 4/5

(ii) tan θ = perpendicular/Base

= AB/BC

= 3x/4x

= ¾

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