Question

ANSWER FAST!!!!!!!

Answer 1

Answer:

The angle between the 190 ft. side and the 330 ft. side is $57.9^o$

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 $\alpha$ is the angle formed by sides a and b (opposite to c), then

$\displaystyle c^2=a^2+b^2-2ab\ cos\alpha$

We'll use the values a=190, b=330, c=280 because we want to compute the angle opposite to c

$\displaystyle cos\alpha =\frac{a^2+b^2-c^2}{2ab}$

$\displaystyle cos\alpha =\frac{190^2+330^2-280^2}{2(190)(330)}$

$\displaystyle cos\alpha =\frac{36100+108900-78400}{125400}$

$\displaystyle cos\alpha =\frac{66600}{125400}=0,5311$

$\displaystyle \alpha= arccos\ 0.5311$

$\boxed{\displaystyle \alpha= 57.9^o}$