Question

In ΔRST, the measure of ∠T=90°, RT = 13, TS = 84, and SR = 85. What ratio represents the sine of ∠S?

Answer 1

`$ \frac{\text{13}}{\text{85}} $`

Explanation:

Given :

ΔRST is a right angled triangle with right angle at ∠RTS.

RT = 13, SR = 85 and TS = 84

We are required to find the ratio that represents the sine of angle RST.

Therefore, using trigonometric ratios, we know that :

`$\sin \angle RST = \frac{\text{perpendicular}}{\text{hypothenuse}} $`

`$\sin \angle RST = \frac{\text{RT}}{\text{RS}} $`

`$\sin \angle RST = \frac{\text{13}}{\text{85}} $`

Therefore, the ratio that represents the sine of of ∠S is
`$ \frac{\text{13}}{\text{85}} $` .