Question

Given: △PTC

Answer 1

Given the the two angles find the missing angle of P which is 30 degrees.

Since angle P and C are identical their sides are congruent.

The hypotenuse, the largest side is PC because it corresponds to angle T

Using Pythagorean Theorem
a^2 + b^2 = c^2

(PT)^2 + (CT)^2 = (PC)^2
Given that PT is 4 and knowing PT and CT are congruent we can rewrite this
(4)^2 + (4)^2 = (PC)^2
PC = rad(32)

Someone fact check plz

Answer 2

Answer:

1.73 units.

Step-by-step explanation:

We have been given that in triangle PTC measure of angle T is 120 degrees and measure of angle C is 30 degrees. We are asked to find the length of side PC.

We will use law of sines to solve for side PC.

$\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}$, where, a ,b and c are opposite sides to angle A, B and C.

Upon substituting our given values in law of sines, we will get:

$\frac{PC}{\text{sin}(120^{\circ})}=\frac{PT}{\text{sin}(30^{\circ})}$

$\frac{PC}{\text{sin}(120^{\circ})}*\text{sin}(120^{\circ})=\frac{4}{\text{sin}(30^{\circ})}*\text{sin}(120^{\circ})$

$PC=\frac{4}{0.5}*0.866025403784$

$PC=2*0.866025403784$

$PC=1.732050807568$

$PC\approx 1.73$

Therefore, the length of side PC is approximately 1.73 units.