Answer:
≈ 50.7 cm²
Step-by-step explanation:
The area (A) of Δ XYZ is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height ), that is
A = [tex]\frac{1}{2}[/tex] × XY × YZ
Calculate YZ using the tangent ratio in the right triangle
tan40° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{x}{11}[/tex] ( multiply both sides by 11 )
11 × tan40° = x , that is
YZ ≈ 9.23 cm
Thus
A = [tex]\frac{1}{2}[/tex] × 11 × 9.23 = 5.5 × 9.23 ≈ 50.7 cm² ( to 3 significant figures )
