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Chapter 10: Q.30 (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 D, are 1213and 513 respectively, and for acute angle E, are513 and 1213 respectively.

Step by step solution

01

Step 1. Given Information.

All the three sides of the triangle are given as 15, 36, and 39. Angle F is given as a right angle.

02

Step 2. Calculation.

Since F is a right angle, the two acute angles are D and E.

It is known that, sinx=perpendicularhypotenuseand cosx=basehypotenuse

Hypotenuse isDE=39.

For Angle D, perpendicular is EF=36and base isDF=15.

So:

SinD=EFDE=3639=1213

And,

CosD=DFDE=1539=513

For Angle E, perpendicular is DF=15and base isEF=36.

SinE=DFDE=1539=513

And,

CosE=EFDE=3639=1213

03

Step 3. Conclusion.

The sine and cosine ratios of the acute angle D, are 1213 and 513 respectively, and sine and cosine ratios of the acute angle E, are 513 and 1213 respectively..

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