A wire is run between two tips of two poles. One pole is 23 ft. taller than the other pole. The poles are 37 ft. apart. How long does the wire need to be to reach between the two poles?
A^2 +B ^2 = C^2
23^2 + 37 ^2 = C^2
529 + 1369 = C^2
1898 = C ^2
Square root both 1898 Calculator.
After you square root it will be C = 43.56
If your draw a sketch of this you will see that a right triangle can be formed.
The base of the right triangle is 37 and the other leg is 23. The hypotenuse is the wire.
Using the Pythagorean theorem,
c^2 = 23^2 + 37^2
Solve for c
To find the length of the wire needed to reach between the two poles, we can use the Pythagorean theorem.
Let's assume the shorter pole's height is x ft.
Given that the taller pole is 23 ft. taller than the shorter pole, its height would be x + 23 ft.
Since the wire runs between the two tips of the poles, it forms a right triangle with the distance between the poles as the base and the height difference between the poles as the perpendicular side.
Using the Pythagorean theorem, we have:
(Base)^2 + (Perpendicular side)^2 = (Hypotenuse)^2
(37 ft)^2 + (x + 23 ft)^2 = (Hypotenuse)^2
Simplifying the equation, we have:
1369 + x^2 + 46x + 529 = (Hypotenuse)^2
Simplifying further, we have:
x^2 + 46x + 1898 = (Hypotenuse)^2
Since we want to find the length of the wire (hypotenuse), we need to find the square root of both sides:
√(x^2 + 46x + 1898) = Hypotenuse
Therefore, the length of the wire needed to reach between the two poles is √(x^2 + 46x + 1898) ft.
To find the length of the wire needed to reach between the two poles, 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 lengths of the other two sides.
In this problem, we can consider the poles as the two sides of a right triangle, and the wire as the hypotenuse. The height difference between the two poles is given as 23 ft, and the distance between the poles is 37 ft. So, let's label the heights of the poles as h1 and h2 (with h2 being the taller pole), and the length of the wire as w.
According to the Pythagorean theorem, we have the equation:
(w^2) = (h1^2) + (h2^2)
Substituting the given information, we have:
(w^2) = (h1^2) + ((h1 + 23)^2)
Simplifying further, we get:
(w^2) = (h1^2) + (h1^2 + 46h1 + 529)
Combining like terms:
(w^2) = 2(h1^2) + 46h1 + 529
Since the distance between the poles is 37 ft, we have:
h1 + h2 = 37
Substituting in h2 = h1 + 23:
h1 + (h1 + 23) = 37
2h1 + 23 = 37
2h1 = 14
h1 = 7
Now, substituting h1 = 7 back into our equation for w^2:
(w^2) = 2(7^2) + 46(7) + 529
(w^2) = 98 + 322 + 529
(w^2) = 949
Taking the square root of both sides, we find:
w = √(949)
Therefore, the wire needs to be approximately 30.82 ft long to reach between the two poles.