body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Core Connections Integrated II, 2015

CC

Core Connections Integrated II, 2015 View details

2. Section 3.2

Continue to next subchapter

Exercise 113 Page 195

Practice makes perfect

a Let's illustrate the situation. We will call the vertical distance between Leon's eyes and the bird x. The pole's total height will therefore be the sum of x and 5.2.

b To find the total distance above the ground we need to determine x. Since we know the adjacent side to the reference angle, and we are looking to determine the opposite side, we can use the tangent ratio.

tan θ=opposite/adjacent Let's identify the opposite and adjacent side to the reference angle in our diagram and write our equation.

Finally, we will solve for x in the equation from the diagram.

tan22^(∘)=x/60

▼

Solve for x

LHS * 60=RHS* 60

60tan22^(∘)=x

Rearrange equation

x=60tan22^(∘)

Use a calculator

x≈ 24.241573...

Round to 2 decimal place(s)

x≈ 24.24

Having found x, we can calculate the total height of the pole. 24.24+5.2=29.44 feet

Subchapter links

3.2.1 Constant Ratios in Right Triangles p.178-180

3.2.2 Connecting Slope Ratios to Specific Angles p.183-184

3.2.3 Expanding the Trig Table p.187-188

3.2.4 Expanding the Trig Table p.192-193

3.2.5 Applying the Tangent Ratio p.195-196