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 cosine of an angle \(x\) is defined as \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(x\) is \(ON = 51\) and the hypotenuse is \(PN=61\). So, \(\cos x=\frac{51}{61}\).

Step2: Solve for \(x\)

Take the inverse cosine (arccos) of both sides. \(x = \cos^{-1}(\frac{51}{61})\). Using a calculator, \(\frac{51}{61}\approx0.8361\). Then \(x=\cos^{-1}(0.8361)\approx33.3^{\circ}\)

Answer:

\(33.3\)