Respuesta :
Answer:
44 degrees.
Step-by-step explanation:
We are asked to find the measure of angle Q using law of cosines.
Law of cosines:
[tex]c^2=a^2+b^2-2ab\times cos(C)[/tex]
Upon substituting our given values in above formula we will get,
[tex]24^2=20^2+34^2-2\times 20\times 34\times cos(Q)[/tex]
[tex]576=400+1156-1360\times cos(Q)[/tex]
[tex]576=1556-1360\times cos(Q)[/tex]
[tex]576-1556=1556-1556-1360\times cos(Q)[/tex]
[tex]-980=-1360\times cos(Q[/tex]
Upon dividing both sides of our equation by -1360 we will get,
[tex]\frac{-980}{-1360}=\frac{-1360\times cos(Q}{-1360}[/tex]
[tex]0.7205882352941176=cos(Q)[/tex]
Now we will use arccos to solve for the measure of angle Q.
[tex]cos^{-1}(0.7205882352941176)=Q[/tex]
[tex]43.896932391182=Q[/tex]
[tex]Q\approx 44[/tex]
Therefore, the measure of angle Q is 44 degrees.
