Solve Right Triangle with Hypotenuse 22 and Angle 37 Degrees

Question

Solve the right triangle (right triangle PQR with right angle at Q, hypotenuse PR=22, $\angle R=37°$). Round decimal answers to the nearest tenth.

Accepted Answer

$PQ \approx 13.2$, $QR \approx 17.6$, $m\angle P = 53°$

Answer

Step 1: Find $\angle P$: Use the angle sum property: $\angle P = 180° - 90° - 37° = 53°$. Step 2: Find PQ (opposite $\angle R$): Use the sine function: $\sin(37°) = \frac{PQ}{22}$, so $PQ = 22 \times \sin(37°) \approx 22 \times 0.6018 \approx 13.2$. Step 3: Find QR (adjacent to $\angle R$): Use the cosine function: $\cos(37°) = \frac{QR}{22}$, so $QR = 22 \times \cos(37°) \approx 22 \times 0.7986 \approx 17.6$.