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Chapter 5: Problem 55

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 measure of the largest angle in the triangle with side lengths 725 feet, 650 feet, and 575 feet is calculated using the Law of Cosines. After substituting the values and simplifying, apply the cosine inverse to find the exact angle in degrees.

Step by step solution

01

Identify Triangle's Sides

Identify the longest side which is 725 feet, and let's call it 'c'. Let the other sides be 'a'=650 feet and 'b'=575 feet.
02

Apply Law of Cosines

The Law of Cosines allows us to solve for an angle when we know all three sides, using the formula \( c^2 = a^2 + b^2 - 2ab \cos(C)\). Rearrange the equation to solve for the cosine of the angle: \(\cos(C) = (a^2 + b^2 - c^2) / (2ab)\).
03

Substitute Values

Substitute the side lengths into the equation: \(\cos(C) =( 650^2 + 575^2 - 725^2) / (2 * 650 * 575)\).
04

Calculate Cosine of Angle

Calculate the value of cosine of C using the above equation.
05

Find Angle

The angle can be found by applying the cosine inverse (also called arccosine) to the result from Step 4. The arccosine can generally be found on most scientific calculators as acos or cos^-1.

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