Exercise 28 Page 429

Let's begin by making a sketch showing us the outline of a baseball field. We mark the home plate with H and the three bases with 1, 2, and 3.

The angle between the path the ball took and the third base foul line, let us call it ∠ H_1, has the measure 27^(∘). We are now looking for the measure of the angle between the ball's path and the first base foul line. Let's call this ∠ H_2. The ∠ H_1 and the ∠ H_2 are complimentary angles. Therefore we know that m∠ H_1 + m∠ H_2 =90^(∘). Let's use this to calculate m∠ H1.

m∠ H_1 + m∠ H_2 =90

Substitute

m∠ H3= 27

27+ m∠ H_2 =90

SubEqn

LHS-27=RHS-27

m∠ H_2 =63

The measure of the angle between the first base foul line and the path of the baseball is 63^(∘).