Question

a worker needs to safely lean a ladder against a wall so that its top reaches 15 feet up the wall. if they lean this ladder such that its base is 8 feet from the wall, whats the length of the ladder? select one of four 15 ft. 24 ft. 17 ft. 23 ft. remaining attempts: 1

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 8\) (distance of the base from the wall), \(b = 15\) (height on the wall), and \(c\) is the length of the ladder.

Step2: Substitute values

Substitute \(a = 8\) and \(b = 15\) into the formula: \(8^{2}+15^{2}=c^{2}\).
Calculate \(8^{2}=64\) and \(15^{2}=225\). Then \(64 + 225=c^{2}\), so \(c^{2}=289\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{289}\). Since \(\sqrt{289}=17\).

Answer:

17 ft.