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

Step-by-step explanation: The triangle YXZ is shown in the figure below.

Area of a triangle is calculated by the formula:

$A=\frac{1}{2} (base*height)$

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:

$sin(68)=\frac{h}{7.3}$

h = 7.3*sin(68)

h = 7.3*0.93

h = 6.8

Now, area of triangle YXZ is

$A=\frac{1}{2} (8.3*6.8)$

A = 28.2

Area of triangle YXZ is 28.2m².