Question

a right triangle has side lengths 7, 24, and 25 as shown below. use these lengths to find tan b, sin b, and cos b.

Explanation:

Step1: Recall trig - ratio definitions

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$ with respect to an angle $\theta$. For angle $B$, the opposite side to $B$ is $AC = 24$, the adjacent side to $B$ is $BC = 7$, and the hypotenuse is $AB=25$.

Step2: Calculate $\tan B$

$\tan B=\frac{\text{opposite to }B}{\text{adjacent to }B}=\frac{24}{7}$

Step3: Calculate $\sin B$

$\sin B=\frac{\text{opposite to }B}{\text{hypotenuse}}=\frac{24}{25}$

Step4: Calculate $\cos B$

$\cos B=\frac{\text{adjacent to }B}{\text{hypotenuse}}=\frac{7}{25}$

Answer:

$\tan B=\frac{24}{7}$, $\sin B=\frac{24}{25}$, $\cos B=\frac{7}{25}$