Question

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

Answer 1

9514 1404 393

Answer:

• c ≈ 13.8 or 2.6 units

Explanation:

The given angle is opposite the shortest of the given sides, so there are two solutions.

Angle B can be found from the law of sines as ...

B = arcsin(b/a·sin(A)) = arcsin(1.25·sin(35°)) ≈ arcsin(0.716971)

B ≈ 45.8° or 134.2°

This means angle C is 180° -35° -45.8° = 10.8°

Then the side c is ...

c = a·sin(C)/sin(A)

c = 8·sin(10.8°)/sin(35°) ≈ 2.6 . . . units

or ...

c = 8·sin(99.2°)/sin(35°) ≈ 13.8 . . . units