A wire runs from the top of a flagpole to a point on the ground that is 9 yards from the base of the pole. The wire is 15 yards long. How many yards tall is the flagpole? (Please type ONLY the numerical answer, no extra spaces or words. Do NOT include any units.)
Think about it. The wire is 9 yards shorter than the flagpole.
You don't need algebra to do this.
height^2 + 9^2 = 15^2
height^2 = 144
height =√144 = 12
To find the height of the flagpole, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the wire is the hypotenuse of the right triangle, and the distance from the base of the pole to the point on the ground is one of the other sides. We can represent the height of the flagpole as the other side.
Using the Pythagorean theorem, we have:
(height of flagpole)^2 + (distance from base to ground)^2 = (wire length)^2
Let's substitute the known values into the equation:
(height of flagpole)^2 + (9 yards)^2 = (15 yards)^2
Simplifying this equation, we have:
(height of flagpole)^2 + 81 yards^2 = 225 yards^2
Rearranging the equation, we get:
(height of flagpole)^2 = 225 yards^2 - 81 yards^2
(height of flagpole)^2 = 144 yards^2
Taking the square root of both sides, we find:
height of flagpole = sqrt(144 yards^2)
Calculating the square root, we get:
height of flagpole ≈ 12 yards
Therefore, the flagpole is approximately 12 yards tall.