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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

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Answer:

[tex]98.25^{\circ}[/tex]

Step-by-step explanation:

[tex]a=3\ \text{feet}[/tex]

[tex]b=4\ \text{feet}[/tex]

[tex]c=5+\dfrac{4}{12}=\dfrac{16}{3}\ \text{feet}[/tex]

[tex]\theta[/tex] = Angle between [tex]a[/tex] and [tex]b[/tex]

From cosine rule we have

[tex]c^2=a^2+b^2-2ab\cos \theta\\\Rightarrow \theta=\cos^{-1}(\dfrac{a^2+b^2-c^2}{2ab})\\\Rightarrow \theta=\cos^{-1}(\dfrac{3^2+4^2-(\dfrac{16}{3})^2}{2\times 3\times 4})\\\Rightarrow \theta=98.25^{\circ}[/tex]

The angle between the walls is [tex]98.25^{\circ}[/tex].

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