Question

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Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). In this right - triangle problem, the ladder length \(c = 50\) ft (hypotenuse), the base \(a=35\) ft, and the height \(h\) is one of the legs (\(b\)). So the formula becomes \(h=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values into the formula

Substitute \(c = 50\) and \(a = 35\) into the formula: \(h=\sqrt{50^{2}-35^{2}}=\sqrt{(50 + 35)(50 - 35)}\) (using the difference of squares \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(h=\sqrt{85\times15}=\sqrt{1275}\). Simplify \(\sqrt{1275}=\sqrt{25\times51}=5\sqrt{51}\approx5\times7.14 = 35.7\) ft.

Answer:

\(h\approx35.7\) ft