A triangular city lot has sides of 225 feet, 190 feet, and 161 feet. Find the angle between the longer two sides of the lot. Round answer to one decimal place.
A)44.7°
B)45.3°
C)79.3°
D)56.1°
E)43.4°

Question

Quizplus · Accepted Answer

To find the angle between the two longer sides (225 feet and 190 feet), we can use the Law of Cosines. The formula is $c^2 = a^2 + b^2 - 2ab\cos(C)$, where $c$ is the side opposite the angle $C$ we want to find, and $a$ and $b$ are the other two sides. Here, $c = 161$ feet, $a = 225$ feet, and $b = 190$ feet. Rearranging the formula to solve for $\cos(C)$, we get $\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$. Plugging in the values and solving for $C$, we find that the angle is approximately 44.7°.

A Triangular City Lot Has Sides of 225 Feet, 190