Question

1. for the following triangle, state the 3 primary trig ratios in relation to angle a.6

Explanation:

Step1: Recall trig - ratio definitions

The three primary trigonometric ratios are sine, cosine, and tangent. For an angle \(A\) in a right - triangle, \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos A = \frac{\text{adjacent}}{\text{hypotenuse}}\), and \(\tan A=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Identify sides relative to angle \(A\)

The side opposite to angle \(A\) is \(BC = 5\), the side adjacent to angle \(A\) is \(AB = 12\), and the hypotenuse is \(AC = 13\).

Step3: Calculate \(\sin A\)

\(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{13}\)

Step4: Calculate \(\cos A\)

\(\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{12}{13}\)

Step5: Calculate \(\tan A\)

\(\tan A=\frac{\text{opposite}}{\text{adjacent}}=\frac{5}{12}\)

Answer:

\(\sin A=\frac{5}{13}\), \(\cos A=\frac{12}{13}\), \(\tan A=\frac{5}{12}\)