Question

in right triangle abc, angles a and b are acute, side ac has a length of 29.5, and tanb = 1/9. what is the length of side bc, rounded to the nearest tenth?
a 870.2
b 265.5
c 5.4
d 3.3

Explanation:

Step1: Recall tangent formula

In right - triangle \(ABC\), \(\tan B=\frac{AC}{BC}\). Given \(\tan B = \frac{1}{9}\) and \(AC = 29.5\).

Step2: Rearrange formula to solve for \(BC\)

From \(\tan B=\frac{AC}{BC}\), we can rewrite it as \(BC=\frac{AC}{\tan B}\).
Substitute \(AC = 29.5\) and \(\tan B=\frac{1}{9}\) into the formula: \(BC = 29.5\div\frac{1}{9}=29.5\times9 = 265.5\)

Answer:

B. 265.5