Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
calculate the value for x.
answer (round to 1 decimal): x = (ie 1.2 or 16.0)

Explanation:

Step1: Identify the trigonometric ratio

We know $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 51^{\circ}$, opposite side to $\theta$ is $x$ and adjacent side is $20$.

Step2: Set up the equation

$\tan(51^{\circ})=\frac{x}{20}$.

Step3: Solve for x

$x = 20\times\tan(51^{\circ})$. Since $\tan(51^{\circ})\approx1.2349$, then $x=20\times1.2349 = 24.698\approx15.8$.

Answer:

$15.8$