Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
19
x
25°
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 $\theta = 25^{\circ}$ and the opposite side to $\theta$ is $x$ and the adjacent side is 19.

Step2: Set up the equation

$\tan(25^{\circ})=\frac{x}{19}$.

Step3: Solve for x

$x = 19\times\tan(25^{\circ})$. Since $\tan(25^{\circ})\approx0.4663$, then $x=19\times0.4663\approx40.7$.

Answer:

$x\approx40.7$