Question

The following figure shows AABC with side lengths to the nearest tenth.B1528C8АFind mZA.Note that mZA is acute. Round to the nearest degree.

Answer 1

Given the triangle, we can find the required angle using the sine rule of triangles. This can be seen below.

Explanation

The sine rule is given as

$\frac{Sin\text{ A}}{a}=\frac{\text{SinB}}{b}$

We can then substitute the given parameters inside the formula.

$\begin{gathered} \frac{\text{SinA}}{15}=\frac{Sin28}{8} \\ \text{SinA}=\frac{15\times Sin28}{8} \\ \text{SinA}=0.8803 \\ A=Sin^{-1}(0.8803) \\ A\approx62^0 \end{gathered}$

Answer:

$A\approx62^0$