Question

A rancher is considering buying a triangular piece of fenced-in land that has sides equal to 500 ft., 800 ft., and 900 ft. He doesn't want any of the corners of the property to be less than 30° or it will be hard to herd the cattle. If this is his only requirement, should he buy this piece of land?

Answer 1

To determine if the triangular piece of land meets the rancher's requirement, we can use the Law of Cosines to calculate the angles of the triangle.

Step-by-step explanation:

In this case, we can use the Law of Cosines to determine whether the triangular piece of land meets the rancher's requirement. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds: c^2 = a^2 + b^2 - 2abcos(C).

For the given triangle with sides of 500 ft., 800 ft., and 900 ft., we can determine the measure of each angle by using the Law of Cosines:

cos(A) = (b^2 + c^2 - a^2) / (2bc) cos(B) = (a^2 + c^2 - b^2) / (2ac) cos(C) = (a^2 + b^2 - c^2) / (2ab)

After calculating the measures of angles A, B, and C, we can determine if any of the angles are less than 30°. If none of the angles are less than 30°, the rancher can buy the piece of land.