An auto dealer wants to string a wire from the top of a pole to the ground and hang colorful pennants from it. The distance from the base of the pole to the point where the wire is attached to the ground is 3 times the height of the pole. If the wire is 63 feet long, how tall is the pole? (hint: draw a diagram, assume the pole is planted perpendicular to the ground).
To solve this problem, we can set up a simple equation using the given information. Let's assume the height of the pole is "h".
According to the information given, the distance from the base of the pole to the point where the wire is attached to the ground is 3 times the height of the pole. Therefore, this distance can be represented as 3h.
We also know that the wire is 63 feet long, so we can set up the following equation based on the Pythagorean theorem:
h^2 + (3h)^2 = 63^2
Expanding the equation, we get:
h^2 + 9h^2 = 3969
Combining like terms, we have:
10h^2 = 3969
To isolate h^2, we divide both sides by 10:
h^2 = 396.9
Taking the square root of both sides, we find:
h ≈ √(396.9)
h ≈ 19.92
Therefore, the pole is approximately 19.92 feet tall.