Given Right ABC with mC90 and mA45 AB8 Find AC a 4 b 8 c 83

Given: Right ABC with mC=90 and mA=45; AB¯¯¯¯¯=8
Find:  AC¯¯¯¯¯

a) 4

b) 8

c) 83

d) 82

e) 42

f) 16

g) None of the above

Solution

Angle B = 180 - 90 - 45 = 45

So, AC = BC as they are opposite to equal sides AC and BC

Since its a right triangle we have

AC^2 + BC^2 = AB^2 ( pythohoras therom)

SO, AB^2 = 8^2 + 8^2 = 128

AB = 8sqrt(2) or answer is d) 82