Question

find the measure of B and a and round each measure to the nearest degree

Answer 1

Step 1

We can find angle B using any of the trigonometric ratios Soh or Cah or Toa. This depends on the data we are given and what we are required to find. Where angle B faces is the opposite. In the question we are given;

$\begin{gathered} Angle\text{ B faces sides 5, hence opposite=5} \\ Hypothenuse\text{ is the longest side=c} \\ The\text{ other side is the adjacent=10} \end{gathered}$

There to find the measure of angle B. we will use Toa written as;

$\begin{gathered} Tan(B)=\frac{opposite}{adjacent} \\ Tan(B)=\frac{5}{10} \end{gathered}$$\begin{gathered} tan(B)=0.5 \\ B=tan^{-1}(0.5)=26.56505118 \\ B\approx27^{\circ} \end{gathered}$

For angle A;

$\begin{gathered} Opposite=10 \\ Adjacent=5 \\ Tan(A)=\frac{10}{5} \\ A=tan^{-1}(2) \\ A=63.43494882 \\ A\approx63^{\circ} \end{gathered}$

Answer;

$\begin{gathered} B=27^{\circ}\text{ to the nearest degree} \\ A=63^{\circ\text{ }}the\text{ nearest degrees} \end{gathered}$