Question

solve for x. round to the nearest tenth of a degree, if necessary. triangle abc with right angle at b, bc = 4.6, ac = 9, angle at c is x degrees

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle \(x\) is defined as \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(x\) is \(BC = 4.6\) and the hypotenuse is \(AC=9\). So, \(\cos x=\frac{4.6}{9}\).

Step2: Calculate the value of \(x\)

We know that \(x = \cos^{-1}(\frac{4.6}{9})\). First, calculate \(\frac{4.6}{9}\approx0.5111\). Then, \(x=\cos^{-1}(0.5111)\). Using a calculator, \(x\approx59.3^{\circ}\).

Answer:

\(x\approx59.3^{\circ}\)