Question

In △ PQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R.

Answer 1

Given: 

In △ PQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. 

To find: the values of sin P, sin R, sec P and sec R. 

Solution: In triangle PQR,∠Q = 90°,

PQ = 4 cm and RQ = 3 cm 

By Pythagoras theorem,

PR² = PQ² +RQ²

RQ² = PR² - PQ²

RQ² = (13)² - (12)²

RQ² = 169 - 144

RQ² = 25

RQ = 5

Use the formula sinθ = perpendicular / hypotenuseSecθ = hypotenuse / base

sin p = \(\frac{QR}{PR}\) = \(\frac{3}{5}\),

sec p = \(\frac{PR}{PQ}\) = \(\frac{5}{4}\),

sec R = \(\frac{PR}{PQ}\) = \(\frac{5}{3}\)

sin R = \(\frac{PQ}{PR}\) = \(\frac{4}{5}\)

NOTE: Always check on which angle you are asked to find any trignometricvalue and take perpendicular,base,hypotenuse accordingly.