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?

Accepted Solution

Answer:The total length of​ the two cables is [tex]2\sqrt{145}\ units[/tex]Step-by-step explanation:see the attached figure to better understand the problemwe know thatIn the right triangle ABDApplying the Pythagoras Theorem[tex]AB^{2}=BD^{2}+AD^{2}[/tex]substitute the given values[tex]AB^{2}=9^{2}+8^{2}[/tex][tex]AB^{2}=145[/tex][tex]AB=\sqrt{145}\ units[/tex]Remember thatAB=AC  ----> because ABC is an isosceles trianglesoThe total length of​ the two cables is equal to[tex]AB+AC=2AB=2\sqrt{145}\ units[/tex]