Question

find the value of \\( \cos u \\) rounded to the nearest hundredth, if necessary.

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). First, find the hypotenuse \(SU\) using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = \sqrt{3}\), \(b=\sqrt{46 - 3}\) (wait, no, correct Pythagorean theorem application: for right - triangle \(STU\) with \(ST=\sqrt{46}\), \(TU = \sqrt{3}\), then \(SU=\sqrt{ST^{2}+TU^{2}}=\sqrt{46 + 3}=\sqrt{49}=7\).

Step2: Calculate \(\cos U\)

For angle \(U\), the adjacent side to \(U\) is \(TU=\sqrt{3}\), and the hypotenuse \(SU = 7\). So \(\cos U=\frac{TU}{SU}=\frac{\sqrt{3}}{7}\approx\frac{1.732}{7}\approx0.25\)

Answer:

\(0.25\)