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5 days ago

Given: △PTC

Mathematics

2 answers:

Leona [12.6K]5 days ago

6 0

Response:

The length of side PC measures 1.73 units.

Detailed steps:

In triangle PTC, we know that angle T is 120 degrees and angle C is 30 degrees. Our goal is to determine the length of side PC.

To find PC, we will employ the law of sines.

$\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}$ Here, a, b, and c correspond to the sides opposite angles A, B, and C, respectively.

By plugging in the known values into the law of sines, we can derive:

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

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

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

$PC=2*0.866025403784$

$PC=1.732050807568$

$PC\approx 1.73$

Thus, side PC's length is approximately 1.73 units.

tester [12.3K]5 days ago

6 0

To determine the missing angle of P, which measures 30 degrees, angle P and C are congruent since they are identical. The longest side, the hypotenuse, is PC, corresponding to angle T. Utilizing the Pythagorean Theorem, a² + b² = c², we find (PT)² + (CT)² = (PC)². Knowing that PT equals 4 and since PT and CT are congruent, we can restate it as (4)² + (4)² = (PC)², leading to PC being equal to rad(32). Could someone please confirm?

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