Question

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 unit.

Answer 1

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.