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World Scholars Arena - Daily Math Problem - 2026-10-13
Today's Challenge, Fully Worked and Independently Verified
Geometry
Advanced Level
Triangle ABC has side AB = 13, side AC = 14, and the included angle BAC = 60°. Find the exact length of side BC, expressed in simplest radical form, using the Law of Cosines.
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- Step 1Apply the Law of Cosines: BC² = AB² + AC² - 2·AB·AC·cos(BAC).
- Step 2BC² = 13² + 14² - 2(13)(14)cos(60°) = 169 + 196 - 364(1/2) = 183.
- Step 3BC = √183.
- Step 4This radicand has no perfect-square factor greater than 1, so the radical is already in simplest form.
Final Answer: BC = √183
How This Problem Was Verified
Every Daily Math Problem is constructed around a known, exact solution, evaluated in closed form, and independently cross-checked by a second numerical method before it is ever published. Disagreement between the two results in rejection, not publication.
Geometry
Category
Advanced
Difficulty Tier
Closed-Form
Derivation Method
MathNet.Numerics
Independent Verification
Suggested Citation
Alexia Network LLC. (2026). World Scholars Arena - Daily Math Problem, 2026-10-13 (Geometry, Advanced level). Retrieved from https://worldscholarsarena.com/daily-math/2026-10-13