Question

In △ABC, m∠A=35 △ A B C , m ∠ A = 35 °, a=8 a = 8 , and b=10 b = 10 . Find c c to the nearest tenth.

Answer 1

`c=13.8\ 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 and solve for sin(B)

`(8)/(sin(35\°))=(10)/(sin(B))`

`sin(B)=sin(35\°)(10)/8`

`B=arcsin(sin(35\°)(10)/8)`

`B=45.8\°`

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 and solve for C

`35\°+45.8\°+C=180\°`

`80.8\°+C=180\°`

`C=180\°-80.8\°=99.2\°`

step 3

Find the measure of side c

Applying the law of sines

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

`(8)/(sin(35\°))=(c)/(sin(99.2\°))`

`c=(8)/(sin(35\°))(sin(99.2\°))}`

`c=13.8\ units`