Problem

If \(\sin{\theta} = 0.6\), find the complement angle \(\theta'\) in degrees.

Answer

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Answer

Substitute \(\theta\) into the formula for \(\theta'\): \(\theta' = 90^\circ - 36.87^\circ\).

Steps

Step 1 ：We know that in a right triangle, the sum of the angles is \(180^\circ\). Therefore, the complement angle \(\theta'\) is defined as \(90^\circ - \theta\).

Step 2 ：To find \(\theta\), we use the inverse sine function, also known as arcsine, as follows: \(\theta = \sin^{-1}(0.6)\).

Step 3 ：By calculating, we find that \(\theta \approx 36.87^\circ\).

Step 4 ：Substitute \(\theta\) into the formula for \(\theta'\): \(\theta' = 90^\circ - 36.87^\circ\).

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