Answer :
The area of the triangle LMN is 20.3 square units
Explanation:
Given that the measurements of the sides of the triangle are [tex]LM=10[/tex] , [tex]LN=5[/tex] and [tex]m\angle L=54^{\circ}[/tex]
We need to determine the area of the triangle.
Area of the triangle:
The area of the triangle can be determined using the formula,
[tex]\text {Area}=\frac{1}{2} mn \sin L[/tex]
Substituting the values, [tex]m=5[/tex], [tex]n=10[/tex] and [tex]m\angle L=54^{\circ}[/tex], we get,
[tex]\text {Area}=\frac{1}{2} (5)(10) \sin 54^{\circ}[/tex]
Simplifying the terms, we have,
[tex]\text {Area}=\frac{1}{2} (5)(10) (0.81)[/tex]
Multiplying the values, we get,
[tex]\text {Area}=\frac{40.5}{2}[/tex]
Dividing, we get,
[tex]Area=20.25[/tex]
Rounding off to the nearest tenth, we get,
[tex]\text {Area}=20.3[/tex]
Thus, the area of the triangle LMN is 20.3 square units.