Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
fill in the missing information.
text should be lower case.
68°
12
tan□=\frac{□}{□}
calculate the value for x.
answer (round to 1 decimal): x = □
(ie 1.2 or 16.0)

Explanation:

Step1: Recall tangent ratio

$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$
In this right - triangle, for the $68^{\circ}$ angle, the opposite side is $12$ and the adjacent side is $x$. So $\tan68^{\circ}=\frac{12}{x}$

Step2: Solve for $x$

We know that $\tan68^{\circ}\approx2.475$. Then from $\tan68^{\circ}=\frac{12}{x}$, we can rewrite it as $x=\frac{12}{\tan68^{\circ}}$.
Substituting the value of $\tan68^{\circ}$, we get $x = \frac{12}{2.475}\approx5.1$

Answer:

$x = 5.1$