Question

To determine whether two interior walls meet at a right angle, carpenters often mark a point 3 feet from the corner on one wall and a point 4 feet from the corner (at the same height) on the other wall. If the straight-line distance between those points is exactly 5 feet, the walls are square. At what angle do the walls meet if the distance measures 5 feet 4 inches

Answer 1

`98.25^(\circ)`

Explanation:

`a=3\ \text{feet}`

`b=4\ \text{feet}`

`c=5+(4)/(12)=(16)/(3)\ \text{feet}`

`\theta` = Angle between
`a` and
`b`

From cosine rule we have

`c^2=a^2+b^2-2ab\cos \theta\\\Rightarrow \theta=\cos^(-1)((a^2+b^2-c^2)/(2ab))\\\Rightarrow \theta=\cos^(-1)((3^2+4^2-((16)/(3))^2)/(2* 3* 4))\\\Rightarrow \theta=98.25^(\circ)`

The angle between the walls is
`98.25^(\circ)`.