Question

QUICK BRAINLEST AND 5 STARS Given: △PTC m∠T=120°, m∠C=30° PT=4 Find: PC.

Answer 1

Given that in △PTC, m∠T=120°, m∠C=30° , PT=4

Now we need to find PC using that information.

We know that sum of all angles in the triangle = 180 degree so we get:

m∠P+m∠T+m∠C=180

m∠P+120+30=180

m∠P+150=180

m∠P=180-150

m∠P=30

Now we can apply sine formula to find the missing side:

$\frac{p}{sin(P)}=\frac{t}{sin(T)}=\frac{c}{sin(C)}$

$\frac{TC}{sin(P)}=\frac{PC}{sin(T)}=\frac{PT}{sin(30)}$

$\frac{TC}{sin(30)}=\frac{PC}{sin(120)}=\frac{4}{sin(30)}$

$\frac{PC}{\frac{\sqrt{3}}{2}}=\frac{4}{\frac{1}{2}}$

$\frac{PC}{\frac{\sqrt{3}}{2}}=8$

$PC=8*\frac{2}{\sqrt{3}}$

$PC=\frac{16}{\sqrt{3}}$

Hence final answer is $PC=\frac{16}{\sqrt{3}}$.

Which is approx 9.24