#### Question

# A triangular piece of land has sides of lengths 725 feet, 650 feet, and 575 feet.?

Find the measure of the largest angle. Please!.

#### Answers

The largest angle will be opposite to the largest side; in this case, the largest angle is opposite to the side that measures 725 feet.

If we take a = 575, b = 650, and c = 725, we want C. Using the Law of Cosines:

c^2 = a^2 + b^2 - 2ab*cos(C)

==> 725^2 = 575^2 + 650^2 - 2(575)(650)cos(C), by substituting in our information

==> cos(C) = (725^2 - 575^2 - 650^2)/[-2(575)(650)] = 7/23, by solving for cos(C)

==> C = arccos(7/23) ≈ 72.3°.

I hope this helps!

The longest angle will be opposite the longest side (let's say c=725). Then, you just need the law of cosines:

If the lengths of the sides are a, b and c and C is the angle opposite side c, then

c^2 = a^2 + b^2 - 2ab * cos(C)

You know what a, b and c are, so plug them in and solve for cos(C). Then you'll need to take the arccos (sometimes written like cos^-1) to cancel the cos. You'll probably need a scientific calculator or Google (you can just type "arccos(x)" after finding cos(C)=x).