Question

The lengths of three sides of a triangle are 10 centimeters, 11 centimeters, and 13 centimeters. Find the measure of the smallest angle of the triangle.

Answer 1

Use law of cosines

• cosX=(b²+c²-a²)/2bc
• cosX=(13²+11²-10²)/2(13)(11)
• cosX=0.66
• X=cos^{-1}(0.66)
• X=48.4°

Answer 2

• 48.4°

Explanation:

The smallest angle is opposite to the smallest side.

Use the law of cosines to find the angle opposite to side with the length of 10 cm:

• cos A = (b² + c² - a²)/(2bc)

• cos x = (11² + 13² - 10²)/(2*11*13)
• cos x = 190/286
• cos x = 0.664 (rounded)
• x = arccos (0.664)
• x = 48.4° (rounded)