Question

find the missing side.
x = ?
round to the nearest tenth.
remember: sohcahtoa

Explanation:

Step1: Identify the trigonometric ratio

We know the adjacent side ($15$) to the given angle ($41^{\circ}$) and we need to find the opposite side ($x$). The trigonometric ratio that relates the opposite and adjacent sides is the tangent ratio. The formula for tangent is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Substitute the values into the formula

Substituting $\theta = 41^{\circ}$, opposite $=x$, and adjacent $ = 15$ into the formula $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, we get $\tan(41^{\circ})=\frac{x}{15}$.

Step3: Solve for $x$

Multiply both sides of the equation by $15$: $x = 15\times\tan(41^{\circ})$.

We know that $\tan(41^{\circ})\approx0.8693$. Then $x=15\times0.8693 = 13.0395$.

Step4: Round to the nearest tenth

Rounding $13.0395$ to the nearest tenth. The digit in the hundredth place is $3$, which is less than $5$. So, $x\approx13.0$.

Answer:

$13.0$