Question

In a ΔABC if ∠B = 90° and Tan C = 5/12, then the length of the hypotenuse is

A) 6 

B) 13 

C) 21 

D) 17

Answer 1

Correct option is: B) 13

Given that \(\angle\) B = \(90^\circ\) & tan C = \(\frac 5{12}\)

\(\because\) tan C = \(\frac {AB}{BC}\)

\(\therefore\) \(\frac {AB}{BC}\) =\(\frac 5{12}\)

= AB = 5 & BC = 12

By applying Pythagoras theorem in \(\triangle\) ABC, we observe

\(AC^2 = AB^2 + BC^2\)

= \(5^2 + 12^2\)

= 24 + 144

= 169 = \(13^2\)

\(\therefore\) AC = 13

Answer 2

Correct option is: B) 13