In △ABC, m∠A=16°, m∠B=49°, and a=4. Find c to the nearest tenth.

c=13.2 units

Step-by-step explanation:

step 1

Find the measure of angle C

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

so

A+B+C=180°

substitute the given values

16°+49°+C=180°

65°+C=180°

C=180°-65°=115°

step 2

Find the measure of c

Applying the law of sines

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

substitute the given values and solve for c

c/sin (115°) = 4/sin (16°)

c=4 (sin (115°)) / sin (16°)

c=13.2 units