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

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

Answer 2

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

Given

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 Pythagoras theorem?

A theorem attributed to Pythagoras is that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

In the right triangle ABD,

By applying the Pythagoras Theorem;

$\rm AB^2=BD^2+AD^2\\\\AB^2=9^2+8^2\\\\AB^2=81+64\\\\AB^2=145\\\\AB=\sqrt{145}$

Therefore,

The total length of​ the two cables is;

$\rm = 2\times AB \\\\ = 2\sqrt{145}$

Hence, the total length of​ the two cables is $2\sqrt{145}$.

To know more about Pythagoras theorem click the link given below.

https://brainly.com/question/5428412