Question

The picture shows a barn door.

A barn door has two parallel bars. A support AB runs across the diagonal between the two parallel bars. The angle made by the diagonal with the parallel bar on top is 45 degrees. The distance between the two parallel bars is 7 feet.

What is the length of the support AB?

Answer 1

"the picture"
you must have used white on white, because I don't see it :S

Answer 2

haha

Answer 3

Nice picture

Answer 4

Using the sketch above. Since we are given that the bars are parallel and the angle the diagonal makes with the top is 45\(^\circ\), we have that angle \(a\) is also 45\(^\circ\), because the upper part of the diagonal is a right-triangle and all angles must sum to 180.

Next, we also know length of side \(x\), because this right-triangle also happens to be isosceles, since we have two angles that are equal. The two sides opposite these equal angles are also equal and so \(x=7\).

The length of \(\overline {AB} \) can be obtained via Pythagoras's Theorem: \( \overline {AB} = \sqrt{7^2+7^2 }=\sqrt{2*49}=7\sqrt{2}\).