Question

g for angle measures of right triangles
which equation can be used to solve for the measure of angle abc?
not drawn to scale
a
10.3 cm
b
2.4 cm
10 cm
c
\\(\sin(x)=\frac{10.3}{10}\\)
\\(\sin(x)=\frac{10}{10.3}\\)
\\(\tan(x)=\frac{10}{2.4}\\)
\\(\tan(x)=\frac{2.4}{10}\\)

Explanation:

Step1: Recall trigonometric - ratio definitions

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

Step2: Analyze sine ratio

$\sin(x)=\frac{AC}{AB}=\frac{2.4}{10.3}$, so the first two sine - related options are incorrect.

Step3: Analyze tangent ratio

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

Answer:

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