# The picture shows a barn door: A barn door has two parallel bars. A support AB of length 6 feet runs across the diagonal between the two parallel bars. The angle made by the diagonal with the parallel bar on top is 60 degrees.? What is the length of

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The picture shows a barn door:

A barn door has two parallel bars. A support AB of length 6 feet runs across the diagonal between the two parallel bars. The angle made by the diagonal with the parallel bar on top is 60 degrees.

What is the length of the bar AC?

6 sin 60°

6 cos 60°

6 divided by cos 60 degrees

6 divided by tan 60 degrees

The picture shows a barn door:

A barn door has two parallel bars. A support AB of length 6 feet runs across the diagonal between the two parallel bars. The angle made by the diagonal with the parallel bar on top is 60 degrees.

What is the length of the bar AC?

6 sin 60°

6 cos 60°

6 divided by cos 60 degrees

6 divided by tan 60 degrees

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To find the length of the barn door's diagonal, you can use trigonometric functions. Since the angle between the diagonal and the parallel bar on top is 60 degrees, and the length of support AB is given as 6 feet, you can use the sine function.

sin(60°) = opposite/hypotenuse sin(60°) = AB/diagonal

Rearranging the equation to solve for the diagonal: diagonal = AB / sin(60°)

Substitute the given value of AB (6 feet) into the equation: diagonal = 6 feet / sin(60°)

Using a calculator, sin(60°) is approximately 0.866: diagonal ≈ 6 feet / 0.866 ≈ 6.928 feet

So, the length of the barn door's diagonal is approximately 6.928 feet.

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