Answer:
The area of the triangle is 22.7 units²
Step-by-step explanation:
We can use trigonometry to find the area of an triangle if we have the length of two sides and the measure of the included angle between them, using the rule A = [tex]\frac{1}{2}[/tex] (a)(b)(sin C), where
- a , b are two sides in the triangle
- C is the angle between the sides a and b
In Δ XYZ
∵ XZ = 11 units
∵ YZ = 8 units
∵ The angle between XZ and YZ is ∠Z
∵ m∠Z = 31°
- We can use the formula of the area above
∴ A = [tex]\frac{1}{2}[/tex] (11)(8)(sin 31)
∴ A = 44 sin 31
∴ A = 22.6616753
- Round it the the nearest tenth
∴ A = 22.7 units²
The area of the triangle is 22.7 units²
