Given,
In triangle ΔXYZ, XY = 8 cm, YZ = 12 cm and area of triangle ΔXYZ is 24cm2
To find: The size of angle ∠XYZ
Let,
angle ∠XYZ be θ
Now using formula
Area of triangle ΔXYZ = \(\frac12XY.YZ\sin\left(\theta\right)\)
Or, 24 = \(\frac12\cdot8\cdot12\cdot\sin\left(\theta\right)\)
Or, \(24=48\cdot\sin\left(\theta\right)\)
Or, \(\frac{24}{48}=\sin\left(\theta\right)\)
Or, \(\frac12=\sin\left(\theta\right)\)
Or, \(\sin\left(30^\circ\right)=\sin\left(\theta\right)\)
Or, 30° = θ
Hence the size of angle ∠XYZ is 30°