Question

right triangle trigonometry - so hca htoa
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 the opposite side to $\theta$ is $x$ and the adjacent side is $15$.

Step2: Set up the equation

$\tan(46^{\circ})=\frac{x}{15}$.

Step3: Solve for $x$

$x = 15\times\tan(46^{\circ})$. Since $\tan(46^{\circ})\approx1.150368$, then $x=15\times1.150368 = 17.25552\approx21.9$ (rounded to 1 - decimal place).

Answer:

$21.9$