Question

The picture shows a barn door:

What is the length of the support AB?

A. 7 over cos 45 degrees
B. 7 tan 45 degrees
C. 7 over sin 45 degrees
D. 7 cos 45 degree

Answer 1

C

Opposite / hypotenuse
Sin 45 degrees= 7/x

Answer 2

Answer: C. 7 over sin 45 degrees

Explanation:

In the given picture, a right triangle is given where the hypotenuse side is AB.

and the side opposite to
`45^(\circ)` is 7 feet.

By using trigonometry in the given figure we can say that

`\sin45^(\circ)=\frac{\text{side opposite to }45^(\circ)}{\text{hypotenuse}}\\\\\Rightarrow\sin45^(\circ)=(7)/(AB)\\\\\Rightarrow AB=(7)/(\sin45^(\circ))`

Hence, the length of the support AB =7 over sin 45 degrees