Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
calculate the value for x.
answer (round to nearest degree): x = □°

Explanation:

Step1: Identify the trigonometric ratio

We know the adjacent side ($a = 18$) and the hypotenuse ($c=20$) of the right - triangle. We use the cosine ratio $\cos(x)=\frac{a}{c}$.
So, $\cos(x)=\frac{18}{20}=0.9$.

Step2: Find the angle

To find the angle $x$, we take the inverse cosine of $0.9$. That is $x = \cos^{-1}(0.9)$.
Using a calculator, $x=\cos^{-1}(0.9)\approx25.84^{\circ}$.

Step3: Round the answer

Rounding $25.84^{\circ}$ to the nearest degree gives $x\approx26^{\circ}$. (Note: if we use the sine - ratio $\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}$, first find the opposite side $b=\sqrt{20^{2}-18^{2}}=\sqrt{400 - 324}=\sqrt{76}\approx8.72$. Then $\sin(x)=\frac{\sqrt{76}}{20}\approx0.436$, and $x=\sin^{-1}(0.436)\approx26^{\circ}$; if we use the tangent - ratio after finding the opposite side, $\tan(x)=\frac{\sqrt{76}}{18}\approx0.484$, and $x = \tan^{-1}(0.484)\approx25.84^{\circ}\approx26^{\circ}$)

Answer:

$x\approx28^{\circ}$