Question

In ΔRST, r = 210 inches, t = 550 inches and ∠T=166°. Find all possible values of ∠R, to the nearest degree.

Answer 1

m(∠R) = 5°

Explanation:

By applying sine rule in the given triangle RST.

`\frac{\text{sin}(\angle R)}{ST}= \frac{\text{sin}(\angle T)}{SR}`

`\frac{\text{sin}(\angle R)}{r}= \frac{\text{sin}(\angle T)}{t}`

`\frac{\text{sin}(\angle R)}{210}= \frac{\text{sin}(166)}{550}`

sin(∠R) =
`\frac{210* \text{sin}(166)}{550}`

= 0.09237

m(∠R) =
`\text{sin}^(-1)(0.09237)`

= 5.3°

≈ 5°