Question

right triangle lmn has a right angle at n. if the value of cos(l) is

, what is the

value of sin(m)?

a

b

c

d

Explanation:

Step1: Recall the co - function identity

In a right triangle \(LMN\) with \(\angle N = 90^{\circ}\), we know that \(\sin(M)=\cos(L)\) (co - function identity: \(\sin\theta=\cos(90^{\circ}-\theta)\) in a right - triangle).

Step2: Use the given value of \(\cos(L)\)

We are given that \(\cos(L)=\frac{\sqrt{21}}{5}\). Since \(\sin(M)=\cos(L)\) (because \(M + L=90^{\circ}\) in right - triangle \(LMN\)).

Answer:

C. \(\frac{\sqrt{21}}{5}\)