Question

score on last try: 0 of 2 pts. see details for more. > next question get a similar question you find the value of x. 20.2 16.6 x° answer x = 31.64 × degrees round to 2 decimal places

Explanation:

Step1: Identify trigonometric ratio

In a right - triangle, for an angle \(x\), \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos x = \frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to angle \(x\) is \(16.6\) and the hypotenuse is \(20.2\). So we use the sine function: \(\sin(x)=\frac{16.6}{20.2}\)

Step2: Calculate the value of \(x\)

First, calculate \(\frac{16.6}{20.2}\approx0.8218\). Then, to find \(x\), we take the inverse sine (arcsin) of \(0.8218\). So \(x = \arcsin(0.8218)\). Using a calculator, \(\arcsin(0.8218)\approx55.30^{\circ}\) (rounded to two decimal places)

Answer:

\(x\approx55.30\)