Given a right triangle with angles $l$ and $m$ (other than the right angle) such that $l+m=90°$, what is the relationship between $sin\left(l\right)$ and $sin\left(m\right)$?

• A. $sin\left(l\right)=cos\left(m\right)$
• B. $sin\left(l\right)=tan\left(m\right)$
• C. $sin\left(l\right)=\frac{1}{sin}$
• D. $sin\left(l\right)=sin\left(m\right)$

Answer: (A)

Verified step by step guidance

1. Recognize that in a right triangle, the two non-right angles \( l \) and \( m \) satisfy the equation \( l + m = 90^\circ \), meaning they are complementary angles.
2. Recall the complementary angle identity in trigonometry: for any angle \( \theta \), \( \sin(90^\circ - \theta) = \cos(\theta) \).
3. Apply this identity to the angles \( l \) and \( m \). Since \( l = 90^\circ - m \), it follows that \( \sin(l) = \sin(90^\circ - m) = \cos(m) \).
4. Understand that this relationship shows the sine of one acute angle in a right triangle is equal to the cosine of the other acute angle.
5. Therefore, among the given options, the correct relationship is \( \sin(l) = \cos(m) \).