Question

if,PQR is right angled triangle at QR=9 cm and PR-PQ = 1cm determine sinR+cosR

Answer 1

Heya,

According to the question,

PQR is a right angled triangle.

QR = 9 cm

PR - PQ = 1 cm
PR = 1 + PQ

By, seeing the fig. we can say that,

=> PQ² + QR² = PR²

=> PQ² + (9)² = (1 + PQ)²

=> PQ² + 81 = PQ² + 1 + 2PQ

=> PQ² - PQ² + 81 - 1 = 2PQ

=> 80 = 2PQ

=> PQ = 40

So, by putting value of PQ, we get

=> PR = 1 + 40

=> PR = 41

Now,

SinR = 40/41
CosR = 9/41

So,
=> SinR + CosR = 40/41 + 9/41

= 49/41. ..... Answer

Hope this helps....:)