Zack, Rachel, and Maddie are unraveling a huge ball of yarn to see how long it is. As they move away from each other, they form a triangle. The distance from Zack to Rachel is 3 meters. The distance from Rachel to Maddie is 2.5 meters. The distance from Maddie to Zack is 4 meters. Find the measures of the three angles in the triangle.

We are tasked to solve the three angles given that we have the measurements of the sides such as

a = Zack to Rachel distance

b = Rachel to Maddie distance

c = Maddie to Zack distance

a = 3

b = 2.5

c = 4

Solving the angles we need to use Law of Cosines:

cos A = 2.5² + 4² - 3² / 2*2.5*4

A = 48.59°

cos B=3² + 4² - 2.5² / 2*3*4

B = 38.625°

C=180 - 48.59° - 38.625°

C = 92.79°

The three angles are 48.59°,38.63° and 92.79°.