A shelf extends perpendicularly 7 inches from a wall. You want to place a brace under the shelf but need to know how far under the shelf to attach the brace to the wall. The angle between the shelf and the brace measures 39°. Which equation and diagram can be used to model this problem?

1. tan 39° = x / 7
2. cos 39° = 7 / x
3. tan 39° = 7 / x
4. sin 39° = 7 / x

Question

A shelf extends perpendicularly 7 inches from a wall. You want to place a brace under the shelf but need to know how far under the shelf to attach the brace to the wall. The angle between the shelf and the brace measures 39°. Which equation and diagram can be used to model this problem?

1. tan 39° = x / 7
2. cos 39° = 7 / x
3. tan 39° = 7 / x
4. sin 39° = 7 / x

Quizzma Team · Answer

To solve this problem, we can use the tangent function because we are dealing with a right triangle formed by the shelf (adjacent side), the brace (hypotenuse), and the vertical distance from the wall to where the brace meets the shelf (opposite side).

The correct equation to model this situation is:

1. tan 39° = x / 7

Here, ( x ) represents the height along the wall where the brace connects, and 7 inches is the length of the shelf extending from the wall. To find ( x ), you rearrange the equation:

[ x = 7 cdot tan(39°) ]

This equation helps you determine how high on the wall you should attach the brace for it to meet the shelf at a 39° angle. If you need further assistance or an in-depth explanation, feel free to check the extended services page!

A shelf extends perpendicularly 7 inches from a wall. You want to place a brace under the shelf but need to know how far under the shelf to attach the brace to the wall. The angle between the shelf and the brace measures 39°. Which equation and diagram can be used to model this problem?

1 Answer