In triangle $MLN$, if side $MN$ is $20$ units, side $LN$ is $24$ units, and the included angle $\angle MLN$ is $60°$, what is the length of chord $ML$?

• A. $26$ units
• B. $30$ units
• C. $24$ units
• D. $20$ units

Answer: (A)

Verified step by step guidance

1. Identify the given elements in triangle MLN: side MN = 20 units, side LN = 24 units, and the included angle ∠MLN = 60° between these two sides.
2. Recall the Law of Cosines formula to find the length of side ML, which is opposite the given angle ∠MLN: \(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\), where \(c\) is the side opposite angle \(C\).
3. Assign the values: let \(a = MN = 20\), \(b = LN = 24\), and \(C = 60^\circ\). Substitute these into the Law of Cosines formula: \(ML^2 = 20^2 + 24^2 - 2 \times 20 \times 24 \times \cos(60^\circ)\).
4. Calculate the cosine of 60 degrees, which is a known value: \(\cos(60^\circ) = 0.5\). Then simplify the expression accordingly without computing the final numeric value.
5. Finally, take the square root of the resulting expression to find the length of side ML: \(ML = \sqrt{20^2 + 24^2 - 2 \times 20 \times 24 \times 0.5}\).