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Core Connections Integrated II, 2015

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Core Connections Integrated II, 2015 View details

2. Section 5.2

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Exercise 116 Page 302

The distance you can calculate with the given values will be 5 feet short of the real height of the building.

≈ 1469 feet

Practice makes perfect

Let's illustrate the situation in a diagram. We will label the height of the Empire State Building x+5. Note that this diagram is not to scale.

With the information given, we can calculate the vertical distance x between Kamillah's eyes and the top of the building using the tangent ratio.

tan θ=opposite/adjacent Let's identify the opposite and adjacent leg to the given angle in our diagram.

Let's solve for x in this equation.

tan 15.5^(∘)=x/5280

LHS * 5280=RHS* 5280

5280tan 15.5^(∘)=x

Rearrange equation

x=5280tan 15.5^(∘)

Use a calculator

x =1464.27359...

Round to nearest integer

x ≈ 1464

The distance between Kamillah's eyes and the top of the Empire State Building is about 1464 feet. To obtain the total distance from the ground, we have to add the distance between the ground and Kamillah's eyes. 1464+5=1469 feet

Subchapter links

5.2.1 Perfect Square Equations p.285-286

5.2.2 Completing the Square p.289

5.2.3 More Completing the Square p.291-292

5.2.4 Introduction to the Quadratic Formula p.296-297

5.2.5 Solving and Applying Quadratic Equations p.301-304

5.2.6 Introducing Complex Numbers p.308-310