Question

In △XYZ , XZ=11 , YZ=8 , and m∠Z=31∘ .

What is the area of the triangle?

Enter your answer, rounded to the nearest tenth of a square unit, in the box.

Answer 1

The area of the triangle is 22.7 units²

Explanation:

The formula of the area of a triangle using trigonometry is A =
`(1)/(2)` (a)(b) sin(C), where a , b are two sides in the triangle and C is the angle between these two sides

In Δ XYZ

∵ XZ = 11 units

∵ YZ = 8 units

∵ m∠Z = 31°

∵ ∠Z is between the two sides XZ and YZ

∴ We can use the formula above to find the area of Δ XYZ

∵ Area Δ XYZ =
`(1)/(2)` (XZ)(YZ) sin(Z)

∴ Area Δ XYZ =
`(1)/(2)` (11)(8) sin(31)

∴ Area Δ XYZ = 22.6616753 unit²

- Round it to the nearest tenth

∴ Area Δ XYZ = 22.7 units²

The area of the triangle is 22.7 units²