Question

The picture shows a barn door:

What is the length of the support AB?
a. 9 divided by tan 60 degrees
b. 9 sin 60°
c. 9 cos 60°
d. 9 divided by sin 60 degrees

Answer 1

d. AB = 9 divided by sin 60 degrees.

Explanation:

Given : picture shown a barn door.

To find : What is the length of the support AB.

Solution : We have given that CB = 9 feet .

angle = 60°,

We need to find AB ?( hypotenuses)

By the trigonometric ratio = sin( theta) =
`(perpendicular\ side)/(hypotnuse)`.

Sin (60) =
`(CB)/(AB)`

Plugging the values of CB = 9

Sin (60 ) =
`(9)/(AB)`.

On multiplying by AB both sides

AB sin(60) = 9

On dividing by sin(60)

AB =
`(9)/(sin(60))`.

Therefore, d. AB = 9 divided by sin 60 degrees.

Answer 2

(D)9 divided by sin 60 degrees

Explanation:

From the given figure, using trigonometry

`(BC)/(AB)=sin60^{{\circ}}`

Substituting the given values, we get

`(9)/(AB)=sin60^{{\circ}}`

`(9)/(sin60^(\circ))=AB`

`AB=\frac{9{*}2}{√(3)}`

`AB=(18)/(√(3))`

`AB=10.4 feet`

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