Question

solve the right triangle. round decimal answers to the nearest tenth.
triangle image with right angle at s, angle at r is 57°, side st is 15, rs ≈ 9.7, m∠t = 33°, rt ≈ □

Explanation:

Step1: Confirm right triangle angles

Sum of angles in triangle is $180^\circ$.
$m\angle T = 180^\circ - 90^\circ - 57^\circ = 33^\circ$

Step2: Calculate hypotenuse $RT$

Use cosine of $\angle R$: $\cos(57^\circ)=\frac{RS}{RT}$ is given, use $\tan(57^\circ)=\frac{ST}{RS}$ to verify $RS$, then use Pythagoras: $RT=\sqrt{RS^2 + ST^2}$
$RS\approx9.7$, $ST=15$, so $RT=\sqrt{9.7^2 + 15^2}=\sqrt{94.09 + 225}=\sqrt{319.09}\approx17.9$

Answer:

$RT\approx 17.9$, $m\angle T=33^\circ$