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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

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 class=

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Answer:

(D)9 divided by sin 60 degrees

Step-by-step explanation:

From the given figure, using trigonometry

[tex]\frac{BC}{AB}=sin60^{{\circ}}[/tex]

Substituting the given values, we get

[tex]\frac{9}{AB}=sin60^{{\circ}}[/tex]

[tex]\frac{9}{sin60^{\circ}}=AB[/tex]

[tex]AB=\frac{9{\times}2}{\sqrt{3}}[/tex]

[tex]AB=\frac{18}{\sqrt{3}}[/tex]

[tex]AB=10.4 feet[/tex]

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

Answer:

d. AB =  9 divided by sin 60 degrees.

Step-by-step 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) = [tex]\frac{perpendicular\ side}{hypotnuse}[/tex].

Sin (60) = [tex]\frac{CB}{AB}[/tex]

Plugging the values of CB = 9

Sin (60 ) = [tex]\frac{9}{AB}[/tex].

On multiplying by AB both sides

AB sin(60) = 9

On dividing by sin(60)

AB = [tex]\frac{9}{sin(60)}[/tex].

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

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