Question

1. find bc

Explanation:

Step1: Find angle B

The sum of angles in a triangle is 180°. So, $\angle B=180^{\circ}-(26^{\circ} + 16^{\circ})=138^{\circ}$.

Step2: Use the Law of Sines

The Law of Sines states that $\frac{BC}{\sin A}=\frac{AC}{\sin B}$. We know $AC = 29$ in, $\angle A=16^{\circ}$, and $\angle B = 138^{\circ}$. So, $BC=\frac{AC\times\sin A}{\sin B}$.

Step3: Substitute values and calculate

$BC=\frac{29\times\sin(16^{\circ})}{\sin(138^{\circ})}$.
$\sin(16^{\circ})\approx0.2756$, $\sin(138^{\circ})\approx0.6691$.
$BC=\frac{29\times0.2756}{0.6691}=\frac{8.0924}{0.6691}\approx12.1$ in.

Answer:

$12.1$ in