Question

Suppose an isosceles triangle ABC has A=pi/4 and b = c = 3. What is the length of a^2. O A. 32(2-2) O B. 32(42 - 2) O C. 322 O D. 32(2 + 2) v

Answer 1

We have:

A = pi/4

b = c = 3

To finde the length a^2 we use the cosine law:

$a^2=b^2+c^2-2bc\cdot\cos A$

Replace the given values

$\begin{gathered} a^2=3^2+3^2-2(3)(3)\cdot\cos \frac{\pi}{4} \\ a^2=9+9-18\cdot\frac{\sqrt[]{2}}{2} \\ a^2=18-9\sqrt[]{2} \\ a^2=9(2-\sqrt[]{2}) \\ a^2=3^2(2-\sqrt[]{2}) \end{gathered}$

Answer: A.