Question

Given: △PTC m∠T=120°, m∠C=30° PT=4 Find: PC.

Answer 1

The law of sines tells you ...

... PC/sin(T) = PT/sin(C)

Multiplying by sin(T), we get ...

... PC = PT·(sin(T)/sin(C))

... PC = 4·sin(120°)/sin(30°) = 4·(√3/2)/(1/2)

... PC = 4√3 ≈ 6.928

Answer 2

Givens

m<T = 120

m<C = 30

PC = 4

Find PC

Solution

4/sin(30) = PC / sin(120)         Note: this is the sine law.

Multiply both sides by sin(120)

$\dfrac{4*sin(120)}{sin(30)} = \text{PC}$

4*0.866/0.5 = PC

Answer

PC= 6.928