Join Talent Academy's exclusive ARML tournament for Loudoun High School students with valid LCPS student IDs. Practice sessions at Brambelton Library from Nov'2023 to May'2024. Open to middle schoolers scoring 90+ in AMC 10. Exciting challenges and prestigious competition await!

Example Problem: Question: In a triangle ABC, the measure of angle A is 60 degrees, and the length of side AB is 8 units. If the length of side AC is 12 units, what is the length of side BC?

Explanation: To find the length of side BC, we can use the Law of Cosines. This law states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those sides and the cosine of the included angle.
In this case, we have side AB with length 8 units and side AC with length 12 units, and angle A measures 60 degrees. Plugging these values into the Law of Cosines equation, we have:

BC^2 = AB^2 + AC^2 - 2(AB)(AC)cos(A)

BC^2 = 8^2 + 12^2 - 2(8)(12)cos(60°)

BC^2 = 64 + 144 - 192(0.5)

BC^2 = 64 + 144 - 96

BC^2 = 112

Taking the square root of both sides, we find:

BC = √112

BC ≈ 10.58 units

Therefore, the length of side BC is approximately 10.58 units.

Being part of the TA ARML contest offers several benefits. Firstly, it provides an opportunity to challenge your problem-solving skills and engage in stimulating mathematical competitions. Secondly, you get to collaborate and form strong connections with like-minded peers who share your passion for mathematics. Additionally, participating in the ARML contest enhances your mathematical knowledge and prepares you for future academic endeavors. It also serves as a valuable addition to your academic profile, showcasing your dedication and proficiency in mathematics.