Question

In △ABC, m∠A=39 △ A B C , m ∠ A = 39 °, a=11 a = 11 , and b=13 b = 13 . Find c c to the nearest tenth.

Answer 1

`c=17.5\ units`

Explanation:

step 1

Find the measure of angle B

Applying the law of sines

`(a)/(sin(A))=(b)/(sin(B))`

substitute the given values

`(11)/(sin(39\°))=(13)/(sin(B))`

`sin(B)={sin(39\°)}(13)/(11)`

`B=arcsin[sin(39\°)(13)/(11)]`

`B=48.1\°`

step 2

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\°`

substitute the given values

`39\°+48.1\°+C=180\°`

`87.1\°+C=180\°`

`C=180\°-87.1\°=92.9\°`

step 3

Find the length side of c

Applying the law of sines

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

substitute the given values

`(11)/(sin(39\°))=(c)/(sin(92.9\°))`

`c=(11)/(sin(39\°))sin(92.9\°)`

`c=17.5\ units`