Question

find uv.

triangle image with right angle at u, side wu labeled √51, angle at v labeled 66°

write your answer as an integer or as a decimal rounded to the nearest tenth.

uv =

submit

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( UWV \), we know \( \angle V = 66^\circ \), \( UW=\sqrt{51} \), and we need to find \( UV \). We can use the tangent function, which is \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). Here, \( \tan(66^\circ)=\frac{UW}{UV} \), so \( UV = \frac{UW}{\tan(66^\circ)} \).

Step2: Calculate \( \sqrt{51} \) and \( \tan(66^\circ) \)

First, \( \sqrt{51}\approx7.1414 \). Then, \( \tan(66^\circ)\approx2.2460 \).

Step3: Compute \( UV \)

Substitute the values into the formula: \( UV=\frac{7.1414}{2.2460}\approx3.2 \).

Answer:

\( 3.2 \)