Question

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 a b * sin(c) 14.7 square units 14.9 square units 15.0 square units 15.3 square units

Explanation:

Step1: Find third side length

Perimeter = XY + YZ + XZ = 24. XY=3, YZ=11, so XZ=24-3-11=10.

Step2: Apply area formula

Area = $\frac{1}{2}ab\sin(C)$. a=XY=3, b=XZ=10, C=102°. Thus Area=$\frac{1}{2}×3×10×\sin(102°)$.

Step3: Calculate and round

$\sin(102°)≈0.9781$. Area≈$\frac{1}{2}×30×0.9781≈14.67≈14.7$.

Answer:

A. 14.7 square units