Question

identifying trig ratios (diagram), level 1
score: 0/3 penalty: none
question
express sin e as a fraction in simplest terms.
answer attempt 1 out of 2
sin e =

Explanation:

Step1: Recall the definition of sine in a right - triangle

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle E\) in right - triangle \(CDE\) with \(\angle D = 90^{\circ}\), the side opposite to \(\angle E\) is \(CD\) and the hypotenuse is \(CE\).

Step2: Calculate the length of the hypotenuse \(CE\)

By the Pythagorean theorem \(CE=\sqrt{CD^{2}+DE^{2}}\). Given \(CD = 2\) and \(DE=9\), then \(CE=\sqrt{2^{2}+9^{2}}=\sqrt{4 + 81}=\sqrt{85}\).

Step3: Find \(\sin E\)

\(\sin E=\frac{CD}{CE}\). Substituting \(CD = 2\) and \(CE=\sqrt{85}\), we get \(\sin E=\frac{2}{\sqrt{85}}\). Rationalizing the denominator: \(\sin E=\frac{2\sqrt{85}}{85}\).

Answer:

\(\frac{2\sqrt{85}}{85}\)