Given:
The measure of three sides of a triangle are 8, 7 and 14.
To find:
The measure of the angle opposite the side of length 8.
Solution:
According to the Law of Cosine:
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
Let a=8, b=7 and c=14, then by using Law of Cosine, we get
[tex]\cos A=\dfrac{7^2+14^2-8^2}{2(7)(14)}[/tex]
[tex]\cos A=\dfrac{49+196-64}{196}[/tex]
[tex]\cos A=\dfrac{181}{196}[/tex]
Taking cos inverse on both sides.
[tex]A=\cos^{-1}\dfrac{181}{196}[/tex]
[tex]A=22.561328[/tex]
[tex]A\approx 22.6[/tex]
Therefore, the measure of the angle opposite the side of length 8 is 22.6 degrees.
