The area of the triangle XYZ is determined as 681.5 in².
How to calculate the area of the triangle?
The area of the triangle is calculated by applying the following formula as shown below;
∠Y = 180 - (∠X + ∠Z) (sum of angles in a triangle)
∠Y = 180 - ( 17 + 72)
∠Y = 91⁰
The length of side XY is calculated using sine rule as follows;
XY / sin Z = XZ / sin Y
XY / sin 72 = 70 / sin 91
XY = (sin 72 / sin 91 ) x 70 in
XY = 66.6 in
The area of the triangle XYZ is calculated as follows;
A = ¹/₂ (XY) (XZ) sin (X)
A = ¹/₂ x 66.6 in x 70 in x sin (17)
A = 681.52 in²
A = 681.5 in² (1 decimal place)