right triangle trigonometry - sohcahtoa\nright triangle trigonometry relates the sides of a right triangle…

Answer:

$40.0$

Explanation:

Step1: Identify the trigonometric ratio

We know $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 30^{\circ}$, adjacent side to $30^{\circ}$ is $20$ and hypotenuse is $x$. So $\cos30^{\circ}=\frac{20}{x}$.

Step2: Recall the value of $\cos30^{\circ}$

$\cos30^{\circ}=\frac{\sqrt{3}}{2}$. Then $\frac{\sqrt{3}}{2}=\frac{20}{x}$.

Step3: Solve for $x$

Cross - multiply gives $x\times\sqrt{3}=20\times2 = 40$. So $x=\frac{40}{\sqrt{3}}$. Rationalize the denominator: $x=\frac{40\sqrt{3}}{3}\approx40.0$.