A triangle has a side a = 4 cm, and angles a = 45° and B = 30°.

Question

A triangle has a side a = 4 cm, and angles a = 45° and B = 30°.

compute angle C

Compute side b.

Answer 1

∠C is easy since there are 180° in all triangles: ∠C = 180° - 45° - 30° = 105°

To find side b, we can use the Law of Sines:

sin(45°)/4 = sin(30°)/b

b•sin(45°) = 4•sin(30°)

b = 4•sin(30°)/sin(45°)

b = 2.828 cm

Answer 2

m∠C = 180º - m∠A - m∠B

Can you calculate and answer?

b / sin 30º = 4 / sin 45º

Can you solve for b and answer?