Question

Use the given information to solve right triangle ABC for all missing parts. Find all parts missing A=31.5°, a =8 1/4 in.

Answer 1

We know two angles and one side of a right triangle. We can find the missing angle as shown below (knowing that the sum of the inner angles of a triangle is equal to 180°)

$\begin{gathered} 180=A+B+C=31.5+B+90 \\ \Rightarrow B=58.5 \end{gathered}$

Finally, we can use the following two trigonometric identities to find the lengths of the missing sides.

$\begin{gathered} \sin A=\frac{a}{c},\tan A=\frac{a}{b} \\ \Rightarrow c=\frac{a}{\sin A},b=\frac{a}{\tan A} \\ \end{gathered}$

Thus,

$\Rightarrow c=15.79,b=\text{13}.46$

The answer are B=58.5°, b=13.46in, c=15.79in