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For a crane to lift the beam shown to the​ right, the beam and the two support cables must form an isosceles triangle with height h. If the distance between the cables along the beam is 18 ft and the height h is 8​ ft, what is the total length of​ the two cables?

User Kunal
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Final answer:

To find the total length of the two cables in an isosceles triangle with height h, we can use the Pythagorean theorem. Substituting the given values, we find the value of h and then calculate the total length.

Step-by-step explanation:

To find the total length of the two cables, we can use the Pythagorean theorem. In an isosceles triangle, the two congruent sides are equal in length. In this case, the distance between the cables along the beam is the base of the triangle and the height h is the length of the congruent sides.

Using the Pythagorean theorem, we can write:

base^2 + h^2 = (2h)^2

Substituting the given values, we have:

18^2 + 8^2 = 2h^2

324 + 64 = 2h^2

388 = 2h^2

h^2 = 194

Taking the square root of both sides, we find:

h = √194

Therefore, the total length of the two cables is 2h, which is 2 times the value of √194.

User Yelizaveta
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