Problem 51 - Algebra and Trigonometry Real Mathematics, Real People

Question

A triangular parcel of ground has sides of lengths 725 feet, 650 feet, and 575 feet. Find the measure of the largest angle.

Step-by-Step Solution

Answer

Taking the arccosine of the value computed, the largest angle of the triangle in degrees is found.

Step 1: Identifying the longest side

First, identify the longest side of the triangle. In this case, it's the side that measures 725 feet.

Step 2: Apply the Law of Cosines

Next, apply the law of cosines to find the measure of the angle opposite the longest side. The law of cosines, in general, can be written as \(c^2 = a^2 + b^2 - 2ab \cdot cos(C)\) where c is the longest side of the triangle and C is the angle opposite the longest side. So in this case, we get \(725^2 = 650^2 + 575^2 - 2 \cdot 650 \cdot 575 \cdot cos(C)\).

Step 3: Solve for C

Rearranging the equation in step 2 to solve for C, we get \(cos(C) = (650^2 + 575^2 - 725^2) / (2 \cdot 650 \cdot 575)\). Calculate the value of cos(C) and then using an arccosine function, find the value of C in degrees.