Question

A triangular playground has sides of lengths 475 feet, 595 feet, and 401 feet. What are the

measures of the angles between the sides, to the nearest tenth of a degree?

Answer 1

To find the measures of the angles between the sides of the triangular playground, we can use the Law of Cosines, which states that:

c^2 = a^2 + b^2 - 2ab cos(C)

where a, b, and c are the side lengths of the triangle, and C is the angle opposite side c. We can use this formula to find the measures of all three angles, as follows:

Angle opposite side 475 feet:

cos(A) = (595^2 + 401^2 - 475^2) / (2 * 595 * 401) = 0.2325
A = cos^-1(0.2325) = 77.3 degrees

Angle opposite side 595 feet:

cos(B) = (475^2 + 401^2 - 595^2) / (2 * 475 * 401) = 0.6921
B = cos^-1(0.6921) = 45.9 degrees

Angle opposite side 401 feet:

cos(C) = (475^2 + 595^2 - 401^2) / (2 * 475 * 595) = 0.8824
C = cos^-1(0.8824) = 28.3 degrees

Therefore, the measures of the angles between the sides of the triangular playground are approximately:

A = 77.3 degrees
B = 45.9 degrees
C = 28.3 degrees