The area of the triangle XYZ is 29.1 square units
Explanation:
Given that the measurements of the sides of the triangle XYZ are [tex]XY = 13[/tex], [tex]XZ=8[/tex] and [tex]m\angle X=34^{\circ}[/tex]
We need to determine the area of the triangle XYZ
Area of the triangle:
The area of the triangle can be determined using the formula,
[tex]Area=\frac{1}{2} yz \ sin X[/tex]
Substituting the values, we get,
[tex]Area=\frac{1}{2}(13)(8) \ sin 34[/tex]
Simplifying, we get,
[tex]Area=\frac{1}{2}(104) (0.56)[/tex]
Multiplying the terms, we get,
[tex]Area=\frac{58.24}{2}[/tex]
Dividing the terms, we have,
[tex]Area=29.12[/tex]
Rounding off to the nearest tenth, we get,
[tex]\text {Area}=29.1[/tex]
Thus, the area of the triangle XYZ is 29.1 square units.
