Question

In triangle RPQ, RP = 8.7 cm PQ = 5.2 cm Angle PRQ = 32° (a) Assuming that angle PQR is an acute angle, calculate the area of triangle RPQ? Give your answer correct to 3 significant figures

Answer 1

`22.6 cm^2(3 " s.f.")`

Explanation:

First, you have to find the angle `RPQ` by using the sine rule.

`8.7/5.2 = (sin \angleRQP)/sin32`

`sin \angleRQP = 87/52sin32`

`\angleRQP = 62.45`

`\therefore \angleRPQ = 180 - 62.45 - 32 = 85.55`

Now, you can use the formula,

`Area = 1/2ab sinC`
`= 1/2 * 8.7 * 5.2 * sin85.55`
`= 22.6 cm^2(3 " s.f.")`

P.S. Thank you @zain-r for pointing my mistake out