Question

troy is building a ramp for his toy cars. the plank he is using for the ramp is 8 feet long and is placed on a 2 - foot - high box. how far from the box is the bottom edge of troys ramp? $sqrt{68}$ 60 6 $sqrt{60}$

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse of a right - triangle, and \(a\) and \(b\) are the other two sides. In this case, \(a = 2\) (height of the box), \(c=8\) (length of the plank/ramp), and we need to find \(b\).
So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 2\) and \(c = 8\) into the formula:
\(b^{2}=8^{2}-2^{2}\)
\(b^{2}=64 - 4\)
\(b^{2}=60\)

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{60}\)

Answer:

\(\sqrt{60}\)