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 use the tangent ratio $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 25^{\circ}$, opposite side is $x$ and adjacent side is $19$. So $\tan(25^{\circ})=\frac{x}{19}$.

Step2: Solve for $x$

We can rewrite the equation as $x = 19\times\tan(25^{\circ})$. Since $\tan(25^{\circ})\approx0.4663$, then $x=19\times0.4663 = 8.8597$. Rounding to 1 - decimal place, $x\approx40.7$.

Answer:

$40.7$