Question

find vw.
u
v
2
27°
w
write your answer as an integer or as a decimal rounded to the nearest tenth.
vw =

Explanation:

Step1: Use trigonometric ratio

In right - triangle \( \triangle UVW\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 27^{\circ}\), the opposite side to \(\angle W\) is \(UV\) and the adjacent side is \(UW = 2\). But we can also use \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Since \(\sin27^{\circ}=\frac{UV}{VW}\) (where \(UV\) is opposite and \(VW\) is hypotenuse), and \(UW = 2\), \(\cos27^{\circ}=\frac{UW}{VW}\).

We know that \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(VW=\frac{UW}{\cos\theta}\).

Step2: Substitute the values

Given \(UW = 2\) and \(\theta = 27^{\circ}\), and \(\cos27^{\circ}\approx0.891\). Then \(VW=\frac{2}{\cos27^{\circ}}\)

$$VW=\frac{2}{0.891}\approx2.2$$

Answer:

\(2.2\)