Question

in the right triangle shown, what is the value of cos a? note: figure not drawn to scale.

Explanation:

Step1: Recall cosine - ratio formula

The cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For angle $A$ in right - triangle $ABC$, the side adjacent to angle $A$ is $AB$ and the hypotenuse is $AC$.

Step2: Identify adjacent and hypotenuse

Given that $AB = 13$ and $AC=30$.

Step3: Calculate $\cos A$

Using the formula $\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}$, we have $\cos A=\frac{AB}{AC}=\frac{13}{30}$.

Answer:

A. $\frac{13}{30}$