In \(\bigtriangleup\) XYZ, XY = 13cm, YZ = 9cm, XZ = 11cm and XYZ = \(\theta\). Find cos\(\theta\)°
The correct answer is D. \(\frac{43}{78}\)
In \(\bigtriangleup\) XYZ, we can use the Law of Cosines to find the cosine of angle XYZ.
The Law of Cosines states that for any triangle with sides of lengths a, b, and c, and the angle opposite side c being \(\gamma\), the following relationship holds: \(c^2 = a^2 + b^2 - 2ab \cos(\gamma)\).
In this case, we have a = 13cm, b = 9cm, and c = 11cm. Substituting these values into the equation above, we get:
\(11^2 = 13^2 + 9^2 - 2 \cdot 13 \cdot 9 \cos(\theta)\)
Solving this equation for \(\cos(\theta)\), we get:
\(\cos(\theta) = \frac{13^2 + 9^2 - 11^2}{2 \cdot 13 \cdot 9} = \frac{43}{78}\)
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