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Chapter 5: Problem 45

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 is the one calculated in the step 3, which is obtained by applying the arctan function to the ratio of the adjacent side length (650 feet) to the opposite side length (575 feet)

Step by step solution

01

Verify Pythagorean relationship.

Calculate \(725^2\), \(650^2\) and \(575^2\). Given that \(725^2 = 650^2 + 575^2\), we can confirm that the triangle is right-angled.
02

Finding the largest angle using tangent.

The tangent of an angle in a right triangle is the ratio of the side opposite the angle to the side adjacent to it. Because the largest angle is opposite the hypotenuse, we have \(tan(\Theta) = \frac{opposite}{adjacent} = \frac{650}{575}\).
03

Solve for the angle.

To find the angle, apply the arctan function to both sides of the equation: \( \Theta = arctan(\frac{650}{575})\). Calculate this value to get the angle in degrees.

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