Question

X, Y and Z form the vertices of a triangle, where ∠ YXZ = 68°, XY = 7.3m and XZ = 8.3m. Calculate the area of the triangle. Round your answer to 1 DP.

Answer 1

Answer: Area = 28.2m²

Explanation: The triangle YXZ is shown in the figure below.

Area of a triangle is calculated by the formula:

`A=(1)/(2) (base*height)`

According to the figure, the base of this triangle is b = 8.3m.

Height is a perpendicular line created from one side and intersecting the opposite angle.

To determine the height, use trigonometric relations to angle 68:

`sin(68)=(h)/(7.3)`

h = 7.3*sin(68)

h = 7.3*0.93

h = 6.8

Now, area of triangle YXZ is

`A=(1)/(2) (8.3*6.8)`

A = 28.2

Area of triangle YXZ is 28.2m².