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!

#1

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).

#2