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=(a)/(c),\tan A=(a)/(b) \\ \Rightarrow c=(a)/(\sin A),b=(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