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
$x = square^{circ}$ submit answer
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Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle OPQ\) with right - angle at \(P\), the side adjacent to angle \(x\) is \(OP = 5.1\) and the hypotenuse is \(OQ=8.9\). We use the cosine ratio. The cosine of an angle in a right - triangle is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos x=\frac{5.1}{8.9}\).

Step2: Solve for \(x\)

Take the inverse cosine (arccos) of both sides. \(x = \cos^{-1}(\frac{5.1}{8.9})\).
Calculate \(\frac{5.1}{8.9}\approx0.573\). Then \(x=\cos^{-1}(0.573)\).
Using a calculator, \(x\approx55.0^{\circ}\)

Answer:

\(55.0\)