Answer:
The angle between the 190 ft. side and the 330 ft. side is [tex]57.9^o[/tex]
Step-by-step explanation:
The Law of Cosines
When we know the value of all sides of a triangle, we can compute all of its interior angles by using the Law of Cosines, which is a generalization of the Pythagoras's theorem. If a,b, and c are the known sides of a triangle and [tex]\alpha[/tex] is the angle formed by sides a and b (opposite to c), then
[tex]\displaystyle c^2=a^2+b^2-2ab\ cos\alpha[/tex]
We'll use the values a=190, b=330, c=280 because we want to compute the angle opposite to c
[tex]\displaystyle cos\alpha =\frac{a^2+b^2-c^2}{2ab}[/tex]
[tex]\displaystyle cos\alpha =\frac{190^2+330^2-280^2}{2(190)(330)}[/tex]
[tex]\displaystyle cos\alpha =\frac{36100+108900-78400}{125400}[/tex]
[tex]\displaystyle cos\alpha =\frac{66600}{125400}=0,5311[/tex]
[tex]\displaystyle \alpha= arccos\ 0.5311[/tex]
[tex]\boxed{\displaystyle \alpha= 57.9^o}[/tex]
