A geometry problem by Mardokay Mosazghi
Geometry
Level
2
In the diagram below, △ABC and △CDE are two right-angled triangles with AC = 24, CE =7 and ∠ ACB = ∠ CED. Find the length of the line segment AE.
The answer is 25.
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1 solution
Let ∠ACB=∠CED=θ. That means that ∠ECD=90∘−θ by the angle sum of △CDE.
That means that △ACE is a right triangle allowing to to apply Pythagoras' Theorem to it. So AE= A C 2 + C E 2 = 2 4 2 + 7 2 = 2 5