In right triangle ABC, we have ∠A = 90◦ , tan B = 2, and BC = 5. What is the length of AB?
B
5
A C
tan B = 2 means that AC/ BA = 2
So AC must be twice as long as BA
Let AB = x so AC = 2x
And using the Pythagorean Theorem
x^2 + (2x)^2 = 5^2
5x^2 = 25
x^2 = 5
x = sqrt (5) = AB
