Question

which equation can be used to solve for the measure of angle abc? not drawn to scale (right triangle abc with right angle at c, ac = 2.4 cm, bc = 10 cm, ab = 10.3 cm, angle at b is ( x )) options: ( \tan(x) = \frac{2.4}{10} ), ( \tan(x) = \frac{10}{2.4} ), ( sin(x) = \frac{10}{10.3} ), ( sin(x) = \frac{10.3}{10} )

Explanation:

Step1: Identify triangle parts

In right triangle \(ABC\), \(\angle C = 90^\circ\), opposite side to \(x\) (angle \(B\)) is \(AC = 2.4\) cm, adjacent side is \(BC = 10\) cm.

Step2: Recall trigonometric ratios

\(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). For \(\theta = x\), \(\tan(x)=\frac{AC}{BC}=\frac{2.4}{10}\).

Answer:

\(\tan(x)=\frac{2.4}{10}\) (the first tan option)