In right triangle ABC, we have ∠A = 90◦ , tan B = 5, and BC = 2. What is the length of AB?
B
2
A C
If tan B = 5.....then the ratio of AC / BA = 5/1 ....so .... AC = 5BA
Using the Pythagorean Theorem
BA^2 + AC^2= BC^2
BA^2 + (5 BA)^2 = 2^2
BA^2 + 25 BA^2 = 4
26 BA^2 = 4
BA^2 = 4 /26 = 2 /13
BA = sqrt (2/13) = 2sqrt (13) / 13 ≈ .392
