Question

Suppose an isosceles triangle ABC has A = 45° and b = c = 4. What is the length of a2? A.22.63

B.54.63
C.9.37
D.3.10

Answer 1

Since b = c, the angles B and C also equal

so you get
180 - 45 = 135
135/2 = =67.5 for each angle

now we know 2 sides and all 3 angles, use the law of sines to find a

b/sin B = a/sin A

4/(sin 67.5) = a/(sin 45)

a = 4(sin 45)/(sin 67.5)

a^2 = (4(sin 45)/(sin 67.5))^2

a^2 = 9.37

Answer is C