Question

problem 1. in the given right triangle find the hypotheuse ab

problem 2. in the given right triangle find the side mk

Explanation:

Step1: Apply Pythagorean theorem for Problem 1

The Pythagorean theorem is \(AB^{2}=AC^{2}+BC^{2}\). Given \(AC = 6\) ft and \(BC=8\) ft.
So \(AB^{2}=6^{2}+8^{2}=36 + 64=100\).

Step2: Solve for \(AB\)

Take the square root of both sides. \(AB=\sqrt{100}=10\) ft.

Step3: Apply Pythagorean theorem for Problem 2

The Pythagorean theorem is \(NK^{2}=MN^{2}+MK^{2}\). Given \(NK = 17\) inches and \(MN = 15\) inches.
So \(MK^{2}=NK^{2}-MN^{2}=17^{2}-15^{2}=(17 + 15)(17-15)=32\times2 = 64\).

Step4: Solve for \(MK\)

Take the square root of both sides. \(MK=\sqrt{64}=8\) inches.

Answer:

Problem 1: \(10\) ft.
Problem 2: \(8\) inches.