Question

Solve the right triangle below and round the decimal answers to the nearest tenth.

Answer 1

We know sum of interior angles in any triangle is 180°. Your specific triangle is a right triangle (one angle must be 90°) and we are also given another angle (57°) that means we can find angle T,

$T=180^{\circ}-90^{\circ}-57^{\circ}=33^{\circ}$

Use the sine function to find $RT$,

$\sin(57^{\circ})=15/RT\implies RT=15/\sin(57^{\circ})\approx17.9$

Use the tangent function to find $RS$,

$\tan(57^{\circ})=15/RS\implies RS=15/\tan(57^{\circ})\approx9.7$

Hope this helps.