Question

using trig to find angles
question
solve for x. round to the nearest tenth of a degree, if necessary.
answer
attempt 1 out of 3
x = 。 submit answer

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle \(x\) is defined as \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the side opposite to angle \(x\) is \(ST = 4.3\) and the hypotenuse is \(US=9.8\). So, \(\sin x=\frac{4.3}{9.8}\).

Step2: Solve for \(x\)

We know that if \(\sin x = a\), then \(x=\sin^{- 1}(a)\). Since \(a = \frac{4.3}{9.8}\approx0.4388\), then \(x=\sin^{-1}(0.4388)\). Using a calculator, \(x\approx26.0^{\circ}\)

Answer:

\(26.0\)