A 60-footpiece of wire is strung between the top of a tower and the ground, making a 30-60-90 triangle. How far from the center of the base of the tower is the wire attached to the ground?How high is the tower?
(The center of the base would be the point where the 90 degrees is)
just did it that way in your previous post
To solve this problem, we can make use of the properties of a 30-60-90 triangle. In a 30-60-90 triangle, the sides are in a specific ratio: the length of the shorter leg (opposite the 30-degree angle) is half the length of the hypotenuse, and the length of the longer leg (opposite the 60-degree angle) is (√3)/2 times the length of the hypotenuse.
Let's denote the length of the shorter leg as x. So, in this case, the hypotenuse would be 2x and the longer leg would be (√3/2)x.
The problem states that the wire is 60 feet long, which is equal to the hypotenuse of the triangle. Therefore, we can set up the following equation:
2x = 60
Now, we can solve this equation to find the value of x:
2x = 60
x = 60/2
x = 30
So, the length of the shorter leg (from the center of the base to where the wire is attached to the ground) is 30 feet.
To find the height of the tower, we need to find the length of the longer leg. Using the (√3/2)x ratio, we can calculate it:
Longer leg = (√3/2)x = (√3/2)(30) = (√3)(15)
So, the height of the tower is (√3)(15) or approximately 25.98 feet.