Question

In the right angle \(△ABC,\ ∠B=90°\), \(tan\ C=\frac {5}{12}\) then the length of hypotenuse is

• A. 16
• B. 13
• C. 21
• D. 17

Answer 1

The Correct Option is B

To solve the problem, we are given:

• Right triangle $ \triangle ABC $ with $ \angle B = 90^\circ $
• Given: $ \tan C = \frac{5}{12} $

1. Understanding $ \tan C $:
In a right triangle, $ \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} $
So, $ \tan C = \frac{AB}{BC} = \frac{5}{12} $

2. Using Pythagoras Theorem:
Let the sides be: - Opposite to $C$ (AB) = 5 units
- Adjacent to $C$ (BC) = 12 units
Then by Pythagoras theorem:
$ \text{Hypotenuse}^2 = AB^2 + BC^2 = 5^2 + 12^2 = 25 + 144 = 169 $
$ \text{Hypotenuse} = \sqrt{169} = 13 $

Final Answer:
The length of the hypotenuse is $ {13} $.