Question

What the answer question

Answer 1

`\bold{A_{_(\Delta XYZ)}=927.5\ cm^2}`

Explanation:

m∠Z = 180° - 118° - 28° = 34°

`\sin(28^o)\approx0.4695\\\\\sin(118^o)=\sin(180^o-62^o)=\sin62^o\approx0.8829 \\\\\sin(34^o)\approx0.5592\\\\`

`\frac{\overline{XY}}{\sin Z}=\frac{\overline{YZ}}{\sin X}\\\\\\\overline{XY}=\frac{\overline{YZ}}{\sin X}\cdot\sin Z\\\\\\\overline{XY}=(42)/(0.4695)\cdot0.5592\\\\\overline{XZ}=50.024281...\\\\\\A_{_(\Delta XYZ)}=\frac12\cdot\overline{XY}\cdot\overline{YZ}\cdot\sin(\angle Z)\\\\\\A_{_(\Delta XYZ)}\approx\frac12\cdot50.0243\cdot42\cdot0.8829=927.4955...\approx927.5`