Question

identifying trig ratios (diagram), level 1
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video examples
express \\( \sin w \\) as a fraction in simplest terms.
answer
attempt 1 out of 3
\\( \sin w = \\)
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Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 18\), \(b=24\).
\(c=\sqrt{18^{2}+24^{2}}=\sqrt{324 + 576}=\sqrt{900}=30\)

Step2: Use the sine formula

The sine of an angle in a right - triangle is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle W\), the opposite side to \(\angle W\) is \(XY = 18\), and the hypotenuse \(WY=30\).
\(\sin W=\frac{18}{30}\)

Step3: Simplify the fraction

Divide numerator and denominator by their greatest common divisor (GCD). The GCD of 18 and 30 is 6.
\(\frac{18\div6}{30\div6}=\frac{3}{5}\)

Answer:

\(\frac{3}{5}\)