Question

find uv.

triangle with right angle at v, angle at u is 34 degrees, side tu is \\(\sqrt{61}\\).

write your answer as an integer or as a decimal rounded to the nearest tenth.
uv = \boxed{}

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 34^{\circ}\), the hypotenuse \(UT=\sqrt{61}\approx7.81\), and the adjacent side to the \(34^{\circ}\) angle is \(UV\). So, \(\cos(34^{\circ})=\frac{UV}{UT}\).

Step2: Solve for \(UV\)

Since \(UT = \sqrt{61}\) and \(\cos(34^{\circ})\approx0.829\), then \(UV=UT\times\cos(34^{\circ})\). Substitute \(UT=\sqrt{61}\) into the formula: \(UV=\sqrt{61}\times\cos(34^{\circ})\approx7.81\times0.829\approx6.5\)

Answer:

\(6.5\)