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Chapter 10: Q.29 (page 541)

Write the sine and cosine ratios for both acute angles of the triangle.

Short Answer

Expert verified

The sine and cosine ratios for the acute angle C, are 45and 35 respectively, and for acute angle B, are35and 45 respectively.

Step by step solution

01

Step 1. Given Information.

All the three sides of the triangle are given as 24, 30, and 18. Angle A is given as a right angle.

02

Step 2. Calculation.

Since A is a right angle, the two acute angles are B and C.

It is known that, sinx=perpendicularhypotenuseand cosx=basehypotenuse

Hypotenuse isBC=30.

For Angle C, perpendicular is AB=24and base isAC=18.

So:

SinC=ABBC=2430=45

And,

CosC=ACBC=1830=35

For Angle B, perpendicular is AC=18and base is AB=24.

SinB=ACBC=1830=35

And,

CosB=ABBC=2430=45

03

Step 3. Conclusion.

The sine and cosine ratios of the acute angle C, are 45 and35 respectively, and sine and cosine ratios of the acute angle B, are 35 and 45 respectively.

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