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

$\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$
In the right - triangle, $\theta = 16^{\circ}$, 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 $\cos16^{\circ}\approx0.96126$. Then $x = 18\times\cos16^{\circ}$.
$x=18\times0.96126 = 17.30268\approx17.3$ (There was a mistake above, it should be $\cos16^{\circ}=\frac{\text{adjacent}}{\text{hypotenuse}}$, adjacent is $x$ and hypotenuse is $18$. Correcting: $x = 18\div\cos16^{\circ}$)
Since $\cos16^{\circ}\approx0.96126$, $x=\frac{18}{\cos16^{\circ}}=\frac{18}{0.96126}\approx18.7$

Answer:

$x = 18.7$