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Chapter 3: Problem 33

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

Short Answer

Expert verified
The largest angle of the triangular parcel is the arccos of calculated \(cos(C)\) value.

Step by step solution

01

Arrange the Triangle Sides

First, recognize that the largest angle in a triangle will be directly opposite the longest side. Therefore, the longest side, 725 feet, is opposite the angle we want to find. Label the triangle sides so that side \(c = 725\), and \(a\) and \(b\) are the other two sides, so \(a = 650\) and \(b = 575\).
02

Apply the Law of Cosines

Put the lengths of the sides into the law of cosines formula and solve for \(cos(C)\). So, \(cos(C) = (a^2 + b^2 - c^2) / (2ab)\) = \((650^2 + 575^2 - 725^2) / (2 * 650 * 575)\). Calculate that to find the value of \(cos(C)\).
03

Find the Angle Measure

To find the measure of the angle in degrees, take the inverse cosine of the \(cos(C)\) value. In the trigonometric terms, the inverse cosine is often referred to as 'arccos.' So, the largest angle \(C = arccos(cos(C))\). Your calculator might provide answer in both degrees and radians, do remember we need to find the measure in degrees. Use a calculator to find the numerical value.

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