Question

WILL BE AWARDED 10 POINTS FOR ANSWER

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

Answer 1

The length of $PC$ will be  $4\sqrt{3}$

Explanation

In triangle $PTC$ , measures of $\angle T = 120$° and $\angle C=30$°

The opposite side of $\angle C$ is $PT$ which is given as 4 and the opposite side of $\angle T$ is $PC$

Suppose, the length of $PC$ is  $x$

Now, according to the Sine rule, we will get........

$\frac{PT}{Sin(C)}=\frac{PC}{Sin(T)}\\ \\ \frac{4}{Sin(30)}=\frac{x}{Sin(120)}\\ \\ x*Sin(30)=4*Sin(120)\\ \\ x= \frac{4*Sin(120)}{Sin(30)}=\frac{4*\frac{\sqrt{3}}{2}}{\frac{1}{2}}=4\sqrt{3}$

So, the length of $PC$ will be  $4\sqrt{3}$

Answer 2

Here we have been given,

m∠T=120°, m∠C=30° PT=4

Let PC = x

Using the law of sines.

$\frac{PT}{Sin30} = \frac{PC}{Sin120}$

$\frac{4}{Sin30} = \frac{x}{Sin120}$

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

$x = 8\times \frac{\sqrt{3} }{2}$

$x= 4\sqrt{3}$

Therefore PC= $4\sqrt{3}$