Multiple Choice
A regular polygon with sides is inscribed in a circle. What is the measure of each interior angle of the polygon?
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2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
Given that = and in a right triangle, what is the value of ?
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Verified step by step guidance1
Recognize that in a right triangle, the two non-right angles are complementary, meaning their measures add up to 90 degrees. So, if \(m\ a\) and \(m\ b\) are the measures of the two acute angles, then \(m\ a + m\ b = 90^\circ\).
Given that \(\cos b = \sin a\), recall the co-function identity in trigonometry: \(\sin \theta = \cos (90^\circ - \theta)\). This means \(\sin a = \cos (90^\circ - a)\).
Since \(\cos b = \sin a\), by the identity above, it follows that \(b = 90^\circ - a\).
You are given \(m\ a = 32^\circ\). Substitute this value into the equation \(b = 90^\circ - a\) to find \(m\ b\).
Calculate \(m\ b = 90^\circ - 32^\circ\) to find the measure of angle \(b\).
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