Question

1. for the following triangle, state the 3 primary trig ratios in relation to angle a.4 application|a=30| thinking|30|

Explanation:

Step1: Recall trig - ratio definitions

The three primary trigonometric ratios are sine, cosine, and tangent. For a right - triangle with respect to an angle $\theta$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify sides with respect to angle $A$

In right - triangle $ABC$ with respect to angle $A$, the opposite side $BC = 5$, the adjacent side $AB = 12$, and the hypotenuse $AC = 13$.

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:

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