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□° = \frac{□}{□}
calculate the value for x.
answer (round to 1 decimal): x = □
(ie 1.2 or 16.0)

Explanation:

Step1: Recall cosine definition

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here the angle $\theta = 16^{\circ}$, the adjacent side to the $16^{\circ}$ angle is $x$ and the hypotenuse is 18. So $\cos16^{\circ}=\frac{x}{18}$.

Step2: Solve for $x$

We know that $x = 18\times\cos16^{\circ}$. Since $\cos16^{\circ}\approx0.9613$, then $x=18\times0.9613 = 17.3034\approx17.3$.

Answer:

For the cosine part: $\cos16^{\circ}=\frac{x}{18}$
For the value of $x$: $x = 17.3$