Question

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

Explanation:

Step1: Recall the definition of tangent in a right triangle

In a right triangle, the tangent of an acute angle is the ratio of the length of the opposite side to the length of the adjacent side. For angle \( B \) in right triangle \( BCD \) (right - angled at \( C \)), we need to identify the opposite and adjacent sides with respect to angle \( B \).

Step2: Identify the sides relative to angle \( B \)

• The side opposite to angle \( B \) is \( CD \), and from the diagram, \( CD = 15 \).
• The side adjacent to angle \( B \) is \( BC \), and from the diagram, \( BC=36 \).

Step3: Calculate \( \tan B \)

Using the formula for tangent, \( \tan B=\frac{\text{opposite}}{\text{adjacent}}=\frac{CD}{BC} \). Substituting the values of \( CD = 15 \) and \( BC = 36 \), we get \( \tan B=\frac{15}{36}\approx0.42 \) (rounded to the nearest hundredth).

Answer:

\( 0.42 \)