Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
37°
19
x
calculate the value for x.
answer (round to 1 decimal): x = (ie 1.2 or 16.0)

Explanation:

Step1: Identify trigonometric ratio

We use tangent since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 37^{\circ}$, opposite side is $19$ and adjacent side is $x$. So $\tan37^{\circ}=\frac{19}{x}$.

Step2: Solve for $x$

We know that $\tan37^{\circ}\approx0.7536$. Then $x=\frac{19}{\tan37^{\circ}}$. Substituting the value of $\tan37^{\circ}$, we get $x=\frac{19}{0.7536}\approx25.2$.

Answer:

$25.2$