In right triangle $LMN$, angles $M$ and $N$ are complementary. If $\sin M=0.759$, what is $\cos N$?

• A. $0.241$
• B. $1.317$
• C. $0.651$
• D. $0.759$

Answer: (D)

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, angle M and angle N satisfy the equation: \(M + N = 90^\circ\).
2. Recall the complementary angle identity in trigonometry: \(\sin(M) = \cos(90^\circ - M)\). Since \(N = 90^\circ - M\), this means \(\sin(M) = \cos(N)\).
3. Given that \(\sin(M) = 0.759\), use the identity to find \(\cos(N)\) by substituting: \(\cos(N) = \sin(M) = 0.759\).
4. Understand that this relationship holds true because sine and cosine of complementary angles are equal, which is a fundamental property in right triangles.
5. Therefore, the value of \(\cos(N)\) is the same as the given \(\sin(M)\), which is 0.759.