Answer:
The Required area of Δ [tex]XYZ[/tex] is [tex]9.6 \ cm^{2}[/tex].
Step-by-step explanation:
Diagram of given scenario is shown below.
Given that,
[tex]XY=5\ cm[/tex], [tex]XZ=6\ cm[/tex] and [tex]\angle X=40[/tex]°
To find : The area of Δ [tex]XYZ[/tex].
So, from the question
Area of triangle when two sides and one angle (between two known sides) are given [tex](Area) = \frac{product \ of \ known\ side \times Sin\angle m}{2}[/tex] , where [tex]\angle m[/tex] is the given angle.
Substituting the given values in above to find area of Δ [tex]XYZ[/tex] we get,
[tex]Ar(\triangle XYZ) = \frac{5\times6\times Sin\angle40}{2}[/tex]
[tex]= 15\times0.642788[/tex]
[tex]= 9.6 \ cm^{2}[/tex]
Therefore, The Required area of Δ [tex]XYZ[/tex] is [tex]9.6 \ cm^{2}[/tex].
