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trig quiz
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question 30 (1 point)
using the appropriate special triangle, determine θ if 0° ≤ θ ≤ 90° for ( 2sqrt{2}sin\theta = 2 ).
a) ( 30^{circ} )
b) ( 90^{circ} )
c) ( 45^{circ} )
d) ( 60^{circ} )
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Explanation:

Step1: Solve for \(\sin\theta\)

Given \(2\sqrt{2}\sin\theta = 2\), divide both sides by \(2\sqrt{2}\).
\(\sin\theta=\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}\)

Step2: Recall special - angle values

We know that for a \(45^{\circ}-45^{\circ}-90^{\circ}\) special triangle, \(\sin45^{\circ}=\frac{1}{\sqrt{2}}\) (since in a right - triangle with angles \(45^{\circ},45^{\circ},90^{\circ}\), if the legs are of length \(a\) and the hypotenuse is \(c = a\sqrt{2}\), then \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), and for \(\theta = 45^{\circ}\), \(\sin45^{\circ}=\frac{a}{a\sqrt{2}}=\frac{1}{\sqrt{2}}\))

Answer:

C. \(45^{\circ}\)