Question

find uv.
triangle with right angle at w, angle at u is 50 degrees, side vw is 4.7. write your answer as an integer or as a decimal rounded to the nearest tenth. uv =

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle UWV \), \( \angle W = 90^\circ \), \( \angle U = 50^\circ \), and \( WV = 4.7 \). We need to find \( UV \) (hypotenuse). The side \( WV \) is opposite to \( \angle U \), so we use the sine function: \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). Here, \( \sin(50^\circ)=\frac{WV}{UV} \).

Step2: Solve for \( UV \)

Rearrange the formula: \( UV = \frac{WV}{\sin(50^\circ)} \). Substitute \( WV = 4.7 \) and \( \sin(50^\circ) \approx 0.7660 \):
\( UV=\frac{4.7}{0.7660} \approx 6.1 \)

Answer:

\( 6.1 \)