Question

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

Answer 1

Answer:

$c=13.1\ units$

Step-by-step 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

$\frac{a}{sin(A)}=\frac{c}{sin(C)}$

substitute

$\frac{11}{sin(57\°)}=\frac{c}{sin(86\°)}$

$c=\frac{11}{sin(57\°)}sin(86\°)$

$c=13.1\ units$