a wire from the top of telephone pole to a point on the ground 6.0m from the pole is 10m long. How high is the pole?
We can solve this problem using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's assume that the height of the pole is H.
Using the given information, we can create a right triangle as follows:
The pole corresponds to one side of the triangle.
The distance from the pole to the ground is the height of the triangle, which is H.
The wire from the top of the pole to a point on the ground forms the hypotenuse of the triangle, which has a length of 10m.
The distance from the pole to the point on the ground, where the wire touches the ground, is one side of the triangle, which is 6.0m.
Now, according to the Pythagorean theorem:
H² + (6.0m)² = (10m)²
H² + 36m² = 100m²
H² = 100m² - 36m²
H² = 64m²
H = √(64m²)
H = 8m
Therefore, the height of the pole is 8.0m.