Question

in the triangle below, b = ______. if necessary, round your answer to two decimal places.

Explanation:

Step1: Find angle B

First, calculate angle at vertex B using the triangle angle sum property (sum of angles in a triangle is $180^\circ$).
$\angle B = 180^\circ - 46.7^\circ - 48^\circ = 85.3^\circ$

Step2: Apply Law of Sines

Use the Law of Sines $\frac{b}{\sin B} = \frac{BC}{\sin A}$ to solve for $b$.
$b = \frac{BC \times \sin B}{\sin A}$

Step3: Substitute values and compute

Plug in $BC=44$, $\angle B=85.3^\circ$, $\angle A=46.7^\circ$.
$b = \frac{44 \times \sin(85.3^\circ)}{\sin(46.7^\circ)} \approx \frac{44 \times 0.9964}{0.7274} \approx 44.73$

Answer:

44.73