Question

set up the problem.
28
47°
x
cos(47°) = x/28
sin(47°) = x/28
cos(47°) = 28/x
tan(47°) = x/28
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dec 1 3:14

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify sides relative to the angle

For the given right - triangle and the angle of $47^{\circ}$, the side opposite to the $47^{\circ}$ angle is $x$ and the side adjacent to the $47^{\circ}$ angle is $28$.

Step3: Apply the tangent ratio

Using the formula $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, with $\theta = 47^{\circ}$, we get $\tan(47)=\frac{x}{28}$.

Answer:

$\tan(47)=\frac{x}{28}$