Exercise 19 Page 218

Let's illustrate the situation. We will call the vertical distance between Mary's and her father's eyes x. The total distance her father's eyes is above the ground will therefore be the sum of x and 32.

To find the total distance above the ground, we need to determine x. To find x, we can use the tangent ratio.

tan( θ)=opposite/adjacent Let's identify the opposite and adjacent side to the 68^(∘) angle in our diagram.

Let's solve for x in the equation from the diagram.

tan68^(∘)=x/15

MultEqn

LHS * 15=RHS* 15

15tan68^(∘)=x

RearrangeEqn

Rearrange equation

x=15tan68^(∘)

UseCalc

Use a calculator

x≈ 37.12630...

RoundDec

Round to 2 decimal place(s)

x≈ 37.13

Having found x, we can calculate the total height of her father's eyes. 37.13+32=69.13 inches