Question

Trigonometry

Answer 1

The area of the triangle XYZ is 29.1 square units

Explanation:

Given that the measurements of the sides of the triangle XYZ are $XY = 13$, $XZ=8$ and $m\angle X=34^{\circ}$

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,

$Area=\frac{1}{2} yz \ sin X$

Substituting the values, we get,

$Area=\frac{1}{2}(13)(8) \ sin 34$

Simplifying, we get,

$Area=\frac{1}{2}(104) (0.56)$

Multiplying the terms, we get,

$Area=\frac{58.24}{2}$

Dividing the terms, we have,

$Area=29.12$

Rounding off to the nearest tenth, we get,

$\text {Area}=29.1$

Thus, the area of the triangle XYZ is 29.1 square units.