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.
calculate the value for x.
answer (round to 1 decimal): x = (ie 1.2 or 16.0)

Explanation:

Step1: Recall tangent definition

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For the given right - triangle with an angle of $68^{\circ}$, the opposite side to the $68^{\circ}$ angle is $x$ and the adjacent side is $12$. So, $\tan68^{\circ}=\frac{x}{12}$.

Step2: Solve for $x$

We know that $\tan68^{\circ}\approx2.475$. From $\tan68^{\circ}=\frac{x}{12}$, we can solve for $x$ by multiplying both sides of the equation by $12$. So, $x = 12\times\tan68^{\circ}$. Substituting the value of $\tan68^{\circ}$, we get $x=12\times2.475 = 29.7$. Rounding to 1 decimal place, $x = 29.6$.

Answer:

1. For the tangent - ratio part: $\tan68^{\circ}=\frac{x}{12}$
2. For the value of $x$: $x = 29.6$