Question

1. 8. applications! draw a picture, then solve for the missing side. round to the nearest tenth. a roofer leaned a 16 - foot ladder against a house. if the base of the ladder is 5 feet from the

Explanation:

Step1: Apply Pythagorean theorem for problem 7

For a right - triangle with sides \(a = 8\), \(c=14\) (where \(c\) is the hypotenuse), and the unknown side \(x\). The Pythagorean theorem is \(a^{2}+x^{2}=c^{2}\), so \(x^{2}=c^{2}-a^{2}\).
Substitute \(a = 8\) and \(c = 14\): \(x^{2}=14^{2}-8^{2}=196 - 64=132\).
Then \(x=\sqrt{132}\approx11.5\).

Step2: Apply Pythagorean theorem for problem 8

For a right - triangle with sides \(a = 6\), \(b = 13\), and the hypotenuse \(x\). The Pythagorean theorem is \(a^{2}+b^{2}=x^{2}\).
Substitute \(a = 6\) and \(b = 13\): \(x^{2}=6^{2}+13^{2}=36+169 = 205\).
Then \(x=\sqrt{205}\approx14.3\).

Answer:

For problem 7: \(x\approx11.5\).
For problem 8: \(x\approx14.3\).