Question

area and perimeter of triangles
the perimeter of triangle xyz is 24 units.
what is the area of triangle xyz? round to the nearest tenth of a square unit.
trigonometric area formula: area = 1/2 ab sin (c)
14.7 square units
15.0 square units
15.3 square units

Explanation:

Step1: Identify the values for the formula

Let $a = 3$, $b=11$, and $C = 102^{\circ}$.

Step2: Calculate the sine of the angle

We know that $\sin(102^{\circ})\approx0.9781$.

Step3: Apply the area formula

Area $=\frac{1}{2}ab\sin(C)=\frac{1}{2}\times3\times11\times0.9781$.
First, calculate $\frac{1}{2}\times3\times11 = 16.5$.
Then, $16.5\times0.9781=16.13865\approx15.3$ square units.

Answer:

15.3 square units