Question

1. a painter leans a ladder against the side of a house. what is d, the distance from the ground to the top of the ladder?
2. what is the value of c in the diagram?

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of the right - triangle and \(c\) is the hypotenuse. In this case, \(a = 9\), \(b=12\).

$$c^{2}=9^{2}+12^{2}$$

Step2: Calculate \(9^{2}\) and \(12^{2}\)

$$9^{2}=81$$

,

$$12^{2}=144$$

So, \(c^{2}=81 + 144\)

Step3: Sum the values

$$c^{2}=225$$

Step4: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (length), \(c=\sqrt{225}\)

Answer:

\(15\)