In ΔEFG, f = 10 inches, g = 61 inches and ∠E=168°. Find the length of e, to the nearest inch.

To solve this problem, we can use the Law of Cosines. The Law of Cosines states that for any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two lengths and the cosine of the included angle.

In this case, we are trying to find the length of side e in triangle EFG. We know the lengths of sides f and g, and the measure of angle E. We can plug these values into the Law of Cosines:

e² = f² + g² - 2fg cos(E) e² = 10² + 61² - 21061 cos(168°)

First, calculate the square of the lengths of sides f and g:

10² = 100 61² = 3721

Then, calculate the cosine of angle E:

cos(168°) = -0.9397

Then, substitute these values back into the equation:

e² = 100 + 3721 - 21061*(-0.9397) e² = 100 + 3721 + 1139.22 e² = 4960.22

Finally, take the square root of both sides to solve for e:

e = √4960.22 e = 70.43

So, the length of side e, to the nearest inch, is approximately 70 inches.