Question

In △ABC, m∠A=57°, m∠B=37°, and a=11. Find c to the nearest tenth.

Answer 1

`c=13.1\ units`

Explanation:

step 1

Find the measure of angle C

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

so

A+B+C=180°

we have

A=57°

B=37°

substitute

57°+37°+C=180°

94°+C=180°

C=180°-94°=86°

step 2

Find the measure of side c

Applying the law of sines

`(a)/(sin(A))=(c)/(sin(C))`

substitute

`(11)/(sin(57\°))=(c)/(sin(86\°))`

`c=(11)/(sin(57\°))sin(86\°)`

`c=13.1\ units`