Question

A triangular plot of land has sides of lengths 420, 350, and 180. Approx. the smallest angle between sides of a triangle

Answer 1

What grade is this for?

Answer 2

11th

Answer 3

Ok, that's what I thought. Well for this, we'll be using the law of cosines. You know what that is?

Answer 4

Yes

Answer 5

Smallest angle is against smallest-side of 180 feet,

Let, the sides are : a=180 ft, b = 350 ft, & c = 420 ft.
By cosin-law,
cosA = (b^2 + c^2 - a^2) / 2bc = (350^2+420^2 -180^2)/2*350*420,
OR,
cosA = (122500+176400 -32400) / = 266500 / 294000 = 0.9065,
Thus,
smallest Angle, A = arccos(0.9065) = 24.98 degrees