Please explain to me what I need to do .
A cable 35 feet long runs from the top of a utility pole to a point on the ground 30 feet from the base of the pole. How tall is the utility pole ?
Pythagorean theorem:
x^2 + 30^2 = 35^2
Solve for x.
To find the height of the utility pole, we can use the Pythagorean theorem. Let's start by understanding the problem and setting up the equation.
Given:
- A cable that is 35 feet long runs from the top of the utility pole to a point on the ground.
- The distance from the base of the pole to the point on the ground is 30 feet.
We want to find:
- The height of the utility pole.
To solve this, we can use the Pythagorean theorem, which 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 cable acts as the hypotenuse, the distance from the base to the point on the ground acts as one side, and the height of the utility pole acts as the other side.
Let's set up the equation:
c^2 = a^2 + b^2
Where:
- c is the length of the cable (35 feet)
- a is the height of the utility pole (what we want to find)
- b is the distance from the base of the pole to the point on the ground (30 feet)
Plugging in the given values, we get:
35^2 = a^2 + 30^2
Simplifying further:
1225 = a^2 + 900
To isolate the height, we subtract 900 from both sides:
325 = a^2
Now, we can take the square root of both sides to find the value of a:
√325 = √(a^2)
18.03 ≈ a
Therefore, the height of the utility pole is approximately 18.03 feet.