Question

Trigonometry

Objective: Use trigonometry functions to find the area of triangles.

In ΔLMN, LM=10, LN=5, and m

Answer 1

The area of the triangle LMN is 20.3 square units

Step-by-step explanation:

Given that the measurements of the sides of the triangle are
`LM=10` ,
`LN=5` and
`m\angle L=54^(\circ)`

We need to determine the area of the triangle.

Area of the triangle:

The area of the triangle can be determined using the formula,

`\text {Area}=(1)/(2) mn \sin L`

Substituting the values,
`m=5`,
`n=10` and
`m\angle L=54^(\circ)`, we get,

`\text {Area}=(1)/(2) (5)(10) \sin 54^(\circ)`

Simplifying the terms, we have,

`\text {Area}=(1)/(2) (5)(10) (0.81)`

Multiplying the values, we get,

`\text {Area}=(40.5)/(2)`

Dividing, we get,

`Area=20.25`

Rounding off to the nearest tenth, we get,

`\text {Area}=20.3`

Thus, the area of the triangle LMN is 20.3 square units.