Question

an angle of a right triangle has a cotangent value of 5/12. complete the statements using the given information and the diagram shown on the right. a = b = c = done

Explanation:

Step1: Recall cotangent definition

$\cot\theta = \frac{\text{adjacent}}{\text{opposite}} = \frac{a}{b} = \frac{5}{12}$
So $a=5k$, $b=12k$ for some $k$. Assume $k=1$ (simplest case).

Step2: Calculate hypotenuse $c$

By Pythagoras: $c = \sqrt{a^2 + b^2} = \sqrt{5^2 + 12^2} = \sqrt{25+144} = \sqrt{169} = 13$

Answer:

$a=5$
$b=12$
$c=13$