Question

solve for x in the triangle. round your answer to the nearest tenth.
$x = \square$
(the triangle is a right triangle with one acute angle of $50^\circ$, the side opposite this angle is 20, and $x$ is the hypotenuse)

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with the opposite side to the 50° angle equal to 20, and \(x\) is the hypotenuse. Use the sine function:
\(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\)

Step2: Substitute known values

Substitute \(\theta = 50^\circ\), opposite = 20, hypotenuse = \(x\):
\(\sin(50^\circ) = \frac{20}{x}\)

Step3: Rearrange to solve for \(x\)

Isolate \(x\) by cross-multiplying:
\(x = \frac{20}{\sin(50^\circ)}\)

Step4: Calculate and round

Use \(\sin(50^\circ) \approx 0.7660\):
\(x \approx \frac{20}{0.7660} \approx 26.1\)

Answer:

26.1