The diagram depicts a rope connecting the top of a pole to the ground. The rope is 27 yd long and
touches the ground 23 yd from the pole. How tall is the pole?
Use the Pythagorean theorem.
To find the height of the pole, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse represents the rope, which is 27 yd long. Let's call the height of the pole "h" and the distance from the pole to the point where the rope touches the ground "d" (23 yd).
Using the Pythagorean theorem, we have:
h^2 + d^2 = rope^2
Substituting in the given values:
h^2 + (23 yd)^2 = (27 yd)^2
Simplifying:
h^2 + 529 yd^2 = 729 yd^2
h^2 = 729 yd^2 - 529 yd^2
h^2 = 200 yd^2
Now, to find the height of the pole, we can take the square root of both sides:
h = √(200 yd^2)
h ≈ 14.14 yd
Therefore, the height of the pole is approximately 14.14 yards.