Answer:
88 degrees.
Step-by-step explanation:
We have been given that a triangle has sides of length 11 m, 12 m, and 16 m. We are asked to find the measure of the angle opposite the side that is 16 m long.
To find the measure of angle opposite to 16 m side, we will use law of cosines.
[tex]c^2=a^2+b^2-2ab\times cos(C)[/tex], where a, b and c represent the side length of triangle. C represents the angle corresponding to side c.
Upon substituting our given values in above formula we will get,
[tex]16^2=11^2+12^2-2\times 11\times 12\times cos(C)[/tex]
[tex]256=121+144-264\times cos(C)[/tex]
[tex]256=265-264\times cos(C)[/tex]
[tex]256-265=265-265-264\times cos(C)[/tex]
[tex]-9=-264\times cos(C)[/tex]
[tex]\frac{-9}{-264}=\frac{-264\times cos(C)}{-264}[/tex]
[tex]\frac{-9}{-264}=cos(C)[/tex]
Now we will use inverse cos formula to solve for C.
[tex]cos^{-1}(\frac{-9}{-264})=C[/tex]
[tex]88.046356247078^{\circ}=C[/tex]
Upon rounding our answer to nearest degree we will get,
[tex]C=88^{\circ}[/tex]
Therefore, the measure of angle opposite to the 16 m long side is 88 degrees.
