Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
30°
20
x
calculate the value for x.
answer (round to 1 decimal): x =
(ie 1.2 or 16.0)

Explanation:

Step1: Identify the trig - 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: Solve for $x$

We know that $\cos30^{\circ}=\frac{\sqrt{3}}{2}$. So, $\frac{\sqrt{3}}{2}=\frac{20}{x}$. Cross - multiplying gives $x\times\sqrt{3}=40$. Then $x = \frac{40}{\sqrt{3}}$. Rationalizing the denominator: $x=\frac{40\sqrt{3}}{3}\approx\frac{40\times1.732}{3}=\frac{69.28}{3}\approx40.0$.

Answer:

$40.0$