Question

solve the triangle.

(a = 113^{\circ}), (c = 20^{\circ}), (c = 250)

(b = 47^{\circ})
(do not round until the final answer. then round to the nearest degree as needed.)

(a \approx \square)
(do not round until the final answer. then round to the nearest tenth as needed.)

(b \approx \square)
(do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Find the missing angle B

$$ B = 180^\circ - A - C = 180^\circ - 113^\circ - 20^\circ = 47^\circ $$

Calculate side a using the Law of Sines

$$ \frac{a}{\sin(A)} = \frac{c}{\sin(C)} \implies a = \frac{c \cdot \sin(A)}{\sin(C)} = \frac{250 \cdot \sin(113^\circ)}{\sin(20^\circ)} \approx 672.9 $$

Calculate side b using the Law of Sines

$$ \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \implies b = \frac{c \cdot \sin(B)}{\sin(C)} = \frac{250 \cdot \sin(47^\circ)}{\sin(20^\circ)} \approx 534.6 $$

Answer:

\(B = 47^\circ\)

\(a \approx 672.9\)

\(b \approx 534.6\)