Given that $\cos b$ = $\sin a$ and $ma=32°$ in a right triangle, what is the value of $mb$?

• A. $58°$
• B. $48°$
• C. $32°$
• D. $90°$

Answer: (A)

Verified step by step guidance

1. 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 \(m\ a + m\ b = 90^\circ\).
2. Given that \(\cos b = \sin a\), recall the co-function identity in trigonometry: \(\sin \theta = \cos (90^\circ - \theta)\). This means \(\sin a = \cos (90^\circ - a)\).
3. Since \(\cos b = \sin a\), by the identity above, it follows that \(b = 90^\circ - a\).
4. You are given \(m\ a = 32^\circ\). Substitute this value into the equation \(b = 90^\circ - a\) to find \(m\ b\).
5. Calculate \(m\ b = 90^\circ - 32^\circ\) to find the measure of angle \(b\).