Trigonometry Objective: Use trigonometry functions to find the area of triangles. In ΔXYZ, XY=13, XZ=8, and m< x=34*. Find the area of ΔXYZ, to the nearest tenth of a square …

Question

asked Aug 27, 2021 200k views

1 Answer

Wolfr · Answer 1 · 2021-09-02T17:11:39+0000

The area of the triangle XYZ is 29.1 square units

Step-by-step 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,

$Area=(1)/(2) yz \ sin X$

Substituting the values, we get,

$Area=(1)/(2)(13)(8) \ sin 34$

Simplifying, we get,

Area=(1)/(2)(104) (0.56)

Multiplying the terms, we get,

Area=(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.