Question

which equation can be used to solve for the measure of angle abc?

( \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: Recall trigonometric ratios

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\) and \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
For angle \(x = \angle ABC\), the opposite side to \(x\) is \(AC = 2.4\) cm and the adjacent side is \(BC=10\) cm. The hypotenuse is \(AB = 10.3\) cm.

Step2: Check \(\tan(x)\)

\(\tan(x)=\frac{\text{opposite}}{\text{adjacent}}=\frac{AC}{BC}\). Substituting \(AC = 2.4\) and \(BC = 10\), we get \(\tan(x)=\frac{2.4}{10}\).

Step3: Check \(\sin(x)\)

\(\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{AC}{AB}\). Substituting \(AC = 2.4\) and \(AB = 10.3\), we get \(\sin(x)=\frac{2.4}{10.3}
eq\frac{10}{10.3}\) and \(\sin(x)
eq\frac{10.3}{10}\) (since \(\text{opposite}<\text{hypotenuse}\) in a right - triangle).

Answer:

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