Question

4.trig - soh - cah - toa_put any 3 two digit numbers to put in the boxes. largest number goes in the hypotenuse box
a. find cos of b as a ratio(fraction)____
b. find tan of a as a ratio(fraction)____

Explanation:

Step1: Recall cosine formula

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

Step2: Determine values for $\cos B$

Let the side $BC = 3$, $AC = 2$ and $AB = 5$. Then $\cos B=\frac{BC}{AB}=\frac{3}{5}$.

Step3: Recall tangent formula

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\tan A$, the opposite side to angle $A$ is $BC$ and the adjacent side is $AC$.

Step4: Determine values for $\tan A$

$\tan A=\frac{BC}{AC}=\frac{3}{2}$.

Answer:

A. $\frac{3}{5}$
B. $\frac{3}{2}$