Question

which equation can be used to solve for the measure of angle abc?
o tan(x) = 2.4/10
o tan(x) = 10/2.4
o sin(x) = 10/10.3
o sin(x) = 10.3/10

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ and $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ for an acute angle $\theta$. For angle $x = \angle ABC$, the opposite side to $\angle ABC$ is $AC = 2.4$ cm and the adjacent side is $BC = 10$ cm.

Step2: Determine the tangent formula for $\angle ABC$

Using the tangent formula $\tan(x)=\frac{\text{opposite}}{\text{adjacent}}$, with opposite side to $\angle ABC$ being $AC = 2.4$ cm and adjacent side $BC = 10$ cm, we get $\tan(x)=\frac{2.4}{10}$.

Answer:

$\tan(x)=\frac{2.4}{10}$