Given:
The sides of each brace have lengths 63 feet, 46 feet, and 40 feet.
To find:
The measure of the angle opposite the 46 foot side.
Solution:
According to the Law of Cosines:
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
We need to find the measure of the angle opposite the 46 foot side. So, [tex]a=46[/tex] and the other sides are [tex]b=63,c=40[/tex].
[tex]\cos A=\dfrac{(63)^2+(40)^2-(46)^2}{2(63)(40)}[/tex]
[tex]\cos A=\dfrac{3969
+1600-2116}{5040}[/tex]
[tex]\cos A=\dfrac{3453}{5040}[/tex]
[tex]\cos A=\dfrac{1151}{1680}[/tex]
Taking cos inverse on both sides, we get
[tex]A=\cos^{-1}\dfrac{1151}{1680}[/tex]
[tex]A=46.75503[/tex]
[tex]A\approx 47[/tex]
Therefore, the measure of the angle opposite the 46 foot side is 47 degrees.
