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.
cos□ = □/□
calculate the value for x.
answer (round to 1 decimal): x = 18.7 (ie 1.2 or 16.0)

Explanation:

Step1: Recall cosine definition

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 16^{\circ}$, the adjacent side to the $16^{\circ}$ angle is 18 and the hypotenuse is $x$. So, $\cos(16^{\circ})=\frac{18}{x}$.

Step2: Solve for $x$

We know that $\cos(16^{\circ})\approx0.96126$. Then, from $\cos(16^{\circ})=\frac{18}{x}$, we can rewrite it as $x=\frac{18}{\cos(16^{\circ})}$. Substituting the value of $\cos(16^{\circ})$, we get $x=\frac{18}{0.96126}\approx18.7$.

Answer:

In the $\cos$ expression, the angle is $16^{\circ}$ and $\cos(16^{\circ})=\frac{18}{x}$, and $x = 18.7$.