Question

which of the following is a correct tangent ratio for the figure? a) tan(76°) = 8/24 b) tan(24°) = 76/8 c) tan(76°) = 24/8

Explanation:

Step1: Recall tangent - ratio formula

In a right - triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$, where $\theta$ is an acute angle.

Step2: Identify opposite and adjacent sides for $\theta = 76^{\circ}$

For the $76^{\circ}$ angle in the given right - triangle, the opposite side has length 24 and the adjacent side has length 8. So, $\tan(76^{\circ})=\frac{24}{8}$.

Step3: Analyze other options

For option A, $\tan(76^{\circ})
eq\frac{8}{24}$. For option B, the other non - right angle in the triangle is $14^{\circ}$ (since $90^{\circ}+76^{\circ}+x = 180^{\circ}$, so $x = 14^{\circ}$), not $24^{\circ}$, and $\tan(24^{\circ})$ is not relevant to the given triangle's side lengths as presented.

Answer:

C. $\tan(76^{\circ})=\frac{24}{8}$