Question

Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of sines, what is the measure of side a? Round your answer to the nearest whole number, if necessary.c = 9 cmA = 22°C = 13°Answers24 cm40 cm5 cm15 cm

Answer 1

Given

There is a triangle with sides a, b, and c and angles A, B, and C.

And,

c = 9 cm

A = 22°

C = 13°

To find:

The value of a.

Explanation:

It is given that,

There is a triangle with sides a, b, and c and angles A, B, and C.

And,

c = 9 cm

A = 22°

C = 13°

That implies,

By using sine law,

$\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \Rightarrow\frac{\sin13\degree}{9}=\frac{\sin22\degree}{a} \\ \Rightarrow a=\frac{9\times\sin22\degree}{\sin13\degree} \\ \Rightarrow a=14.9875 \\ \Rightarrow a=15cm \end{gathered}$

Hence, the value of a is 15cm.