Question

question find the value of tan b rounded to the nearest hundredth, if necessary.

Explanation:

Step1: Recall the tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For angle $B$, the side opposite to angle $B$ is $CD = 15$, and the side adjacent to angle $B$ is $BC=36$.

Step2: Calculate the tangent value

Using the formula $\tan B=\frac{CD}{BC}$, substitute $CD = 15$ and $BC = 36$. So, $\tan B=\frac{15}{36}$.

Step3: Simplify the fraction

Simplify $\frac{15}{36}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3. $\frac{15\div3}{36\div3}=\frac{5}{12}\approx0.42$

Answer:

$0.42$