Question

what is sec(∠a)? reduce fractional answers to lowest terms.
(diagram: right triangle ( abc ) with right angle at ( c ), ( ac = 5 ), ( cb = 12 ), ( ab = 13 ))

Explanation:

Step1: Recall secant definition

$\sec(\theta) = \frac{1}{\cos(\theta)}$, and $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ for a right triangle. So $\sec(\theta) = \frac{\text{hypotenuse}}{\text{adjacent}}$.

Step2: Identify sides for $\angle A$

In $\triangle ABC$, right - angled at $C$, for $\angle A$:

• Adjacent side to $\angle A$ is $AC = 5$.
• Hypotenuse is $AB = 13$.

Step3: Calculate $\sec(\angle A)$

Using the formula $\sec(\angle A)=\frac{\text{hypotenuse}}{\text{adjacent}}$, we substitute the values: $\sec(\angle A)=\frac{AB}{AC}=\frac{13}{5}$.

Answer:

$\frac{13}{5}$