Question

identifying trig ratios (diagram), level 1
question
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find the value of sin q rounded to the nearest hundredth, if necessary.
answer
attempt 1 out of 3
sin q =
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Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 10\), \(b=24\).
\(QS=\sqrt{QR^{2}+RS^{2}}=\sqrt{24^{2}+10^{2}}=\sqrt{576 + 100}=\sqrt{676}=26\)

Step2: Use the sine formula

The sine of an angle in a right - triangle is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle Q\), the opposite side to \(\angle Q\) is \(RS = 10\), and the hypotenuse is \(QS=26\).
\(\sin Q=\frac{RS}{QS}=\frac{10}{26}\approx0.38\)

Answer:

\(0.38\)