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 = ∘
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Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, for angle \(x\), the opposite side is \(GF = 48\) and the hypotenuse is \(GE=60\). So, \(\sin x=\frac{48}{60}\).

Step2: Simplify the ratio

Simplify \(\frac{48}{60}\) to \(\frac{4}{5}=0.8\). So, \(\sin x = 0.8\).

Step3: Find the angle

To find \(x\), use the inverse sine function \(x=\sin^{- 1}(0.8)\). Using a calculator, \(x=\sin^{-1}(0.8)\approx53.1^{\circ}\).

Answer:

\(53.1\)