Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
15
46°
x
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 $\theta = 46^{\circ}$ and opposite side is $15$, adjacent side is $x$. So $\tan46^{\circ}=\frac{15}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{15}{\tan46^{\circ}}$. Since $\tan46^{\circ}\approx1.03553$, then $x=\frac{15}{1.03553}\approx14.5$.

Answer:

$14.5$