In the triangle ABC, we know that B = 45 °, D is the point on BC, ad = 7, AC = 8, DC = 3, and find the length of ab

Make AE ⊥ BC at point E
Let de = X
Then AE ^ 2 = 5 ^ 2-x ^ 2 = 7 ^ 2 - (3 + x) ^ 2
That is, 5 ^ 2-x ^ 2 = 7 ^ 2 - (3 + x) ^ 2
The solution is de = 2.5
In RT △ AED, AE = 2.5 √ 3 according to Pythagorean theorem
∵∠B=45°
∴AB=√2AE=2.5*√6

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