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 60 degrees. The distance between the two parallel bars is 9 feet. What is the length of the support AB? 9 divided by tan 60 degrees 9 sin 60° 9 cos 60° 9 divided by sin 60 degrees

Answer 1

Answer:

$AB= \frac{9}{sin 60^{\circ}}$

Step-by-step explanation:

REFER THE ATTACHED FIGURE

Given :

AC and DB are parallel bars .

AB is the diagonal between two parallel bars .

The angle made by the diagonal with the parallel bar on top is 60 degrees.

The distance between the two parallel bars is 9 feet.

To Find : What is the length of the support AB?

Solution :

For ∠BAC = 60° base is AC and perpendicular is BC

Using trigonometric ratios i.e.

$sin\theta = \frac{perpendicular}{hypotenuse}$

$sin 60^{\circ}= \frac{BC}{AB}$

$sin 60^{\circ}= \frac{9}{AB}$

$AB= \frac{9}{sin 60^{\circ}}$

Thus Option 4 is correct

Length of support AB = 9 divided by sin 60 degrees

Answer 2

The length of the support AB is 9 divided by sin 60 degrees.