Answer: The acute angle ∠YXZ = 24.3°.
Step-by-step explanation:
If in triangle ABC, C is the angle included between sides a and b then
Area of triangle = [tex]\dfrac12a\cdot b\cdot sin C[/tex]
here, XZ = 21.5cm and XY = 13.5cm are sides that includes acute angle ∠YXZ..
Area of a triangle = 59.7cm²
then, as per given, we have
[tex]59.7=\dfrac12(21.5)(13.5)\ \sin X\\\\\Rightarrow\ 59.7=145.125\ \sin X\\\\\Rightarrow\ \sin X = \dfrac{59.7}{145.125}\\\\\Rightarrow\ \sin X =0.41137\\\\\Rightarrow\ X = \sin ^{-1}(0.41137)\approx24.3^{\circ}[/tex]
Hence, the acute angle ∠YXZ = 24.3°.
