Question

A triangular plot of land has sides of lengths 420 feet, 330 feet, and 180 feet. Approximate the smallest angle between the sides. The choices are rounded to the nearest degree.

A. 30 degree
B. 27 degree
C. 22 degree
D. 24 degree

Answer 1

D. 24 degree

Explanation:

Sides of the triangle are

a = 330 ft

b = 180 ft

c = 420 ft

From cosine rule we have

`\angle A=\cos^(-1)((b^2+c^2-a^2)/(2bc))\\ =\cos^(-1)((180^2+420^2-330^2)/(2*180* 420))\\ =48.65^(\circ)`

`\angle B=\cos^(-1)((a^2+c^2-b^2)/(2ac))\\ =\cos^(-1)((330^2+420^2-180^2)/(2* 330* 420))\\ =24.17^(\circ)`

`\angle C=\cos^(-1)((a^2+b^2-c^2)/(2ab))\\ =\cos^(-1)((330^2+180^2-420^2)/(2* 330* 180))\\ =107.19^(\circ)`

The smallest angle in the triangle is
`\angle B=24.17^(\circ)`.