In a circus a tightrope is stretched from the top of a 10 ft. pole to the top of a 25 ft pole. The poles are 36 feet apart and vertical. How long is the tightrope?
Show your work.
the height difference is 15 ft.
So, now just use the Pythagorean Theorem for a triangle with legs of 15 and 36
Hint: Recall that one of your standard right triangles is 5-12-13
To find the length of the tightrope, we can use the Pythagorean theorem. The 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 two poles and the tightrope form a right triangle. The distance between the poles (36 feet) is the base of the triangle. The height of the triangle is the difference in height between the two poles (25 ft - 10 ft = 15 ft).
Let's label the base as 'b', the height as 'h', and the hypotenuse (length of the tightrope) as 'c'.
According to the Pythagorean theorem: c^2 = b^2 + h^2
Plugging in the values we know:
c^2 = 36^2 + 15^2
Simplifying the equation:
c^2 = 1296 + 225
c^2 = 1521
To find the value of 'c', we need to find the square root of both sides:
c = √(1521)
Calculating the square root:
c = 39
So, the length of the tightrope is 39 feet.