Question

in a right ∆PQR ,right angled at Q,PR-PQ=1cm and QR =5cm. find the values of sin R, cos R and tan R.​

Answer 1

Answer:

Refer the above figure

In a right angled triangle we know that

Base² + Perpendicular ² = Hypotenuse²

As PR - PQ = 1

PR = PQ + 1

Or

PQ = PR - 1

Therefore in the terms of x

Let the unknown sides PQ and PR be x-1 and x respectively.

Now,

Using the Pythagoras theorem,

We know that,

PQ²+ QR² = PR²

(x-1)² + 5² = x²

x² - 2x + 1 + 25 = x²

2x = 26

x = 13.

x-1 = 12

As we know that

sin = perpendicular /hypotenuse.

Sin R = 12 / 13.

Cos = base /perpendicular.

Cos R = 5/ 13.

Tan = perpendicular /base.

Tan R = 12 / 5.

Hope it helps you dear.

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