Question

find vw.
write your answer as an integer or as a decimal rounded to the nearest tenth.
vw =
submit
work it out
not feeling ready yet? these can help:
multiply radical expressions
lesson: trigonometric ratios
trigonometric functions of special angles
proportions

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( VWU \), \( \angle V = 69^\circ \), hypotenuse \( UV=\sqrt{47} \), and \( VW \) is adjacent to \( \angle V \). Use cosine: \( \cos(69^\circ)=\frac{VW}{UV} \).

Step2: Substitute values and solve

\( UV = \sqrt{47}\approx6.8557 \), so \( VW = UV\times\cos(69^\circ) \). Calculate \( \cos(69^\circ)\approx0.3584 \), then \( VW\approx6.8557\times0.3584\approx2.46 \approx 2.5 \) (rounded to nearest tenth).

Answer:

\( 2.5 \)