MATH SOLVE

3 months ago

Q:
# 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

A:

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]