Three coins

Question

Three coins are placed on a table such that they just touch each other. The diameters of the coins are 1.8cm, 2.2cm, and 3 cm. Solve the triangle where vertices are the centers of the coins.

Answer 1

Begin by making a sketch of three circles, having radii 0.9, 1.1 & 1.5 cm each. 

Draw the three line segments joining centers, two at a time, thus forming a triangle with sides

1.1+1.5 cm, 1.1+0.9 cm, and 1.5+0.9 cm.

 

Now you know all the three side lengths of this triangle; you may use the Law of Sines to calculate the triangle's angles.

Advice: calculate the largest angle first (it's across from the largest side).