Question

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?

Answer 1

Answer:

The total length of​ the two cables is $2\sqrt{145}\ units$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABD

Applying the Pythagoras Theorem

$AB^{2}=BD^{2}+AD^{2}$

substitute the given values

$AB^{2}=9^{2}+8^{2}$

$AB^{2}=145$

$AB=\sqrt{145}\ units$

Remember that

AB=AC  ----> because ABC is an isosceles triangle

so

The total length of​ the two cables is equal to

$AB+AC=2AB=2\sqrt{145}\ units$