Question

suppose an isosceles triangle abc has ( a=\frac{pi}{4} ) and ( b = c = 4 ). what is the length of ( a^{2} )?

a. ( 4^{2}(sqrt{2}-2) )
b. ( 4^{2}(2+sqrt{2}) )
c. ( 4^{2} sqrt{2} )
d. ( 4^{2}(2-sqrt{2}) )

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines states that \(a^{2}=b^{2}+c^{2}-2bc\cos A\). Given \(b = c = 4\) and \(A=\frac{\pi}{4}\), substitute these values into the formula.

$$
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$$

Step2: Simplify the expression

$$
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$$

Answer:

D. \(4^{2}(2 - \sqrt{2})\)