Trigonometry Alg. 2

Question

Introduction

Sally had just got her license and the first night her parents said she could drive, she came home and her little dog ran in front of her. To avoid her dog, she smashed into the side of the house. After everyone was determined to be OK, she had the fun of repairing the damage to the house. 

She offered to paint the side of the house for her parents. Her parents left it up to her to buy the paint and do all the work. Using her amazing Algebra 2 skills she thought she’d calculate what to buy. The first step was to determine how much paint she would need. 

First, she needed to determine the surface area of the side of the house in order to estimate the number of gallons of paint she would need. She knew the top of the house was an isosceles triangle. She figured she could climb on a ladder to measure the angle between the pitch of the roof and the wall, and the rest was pretty easy.

Using composite figures and trigonometry she calculated the area of the side of the house.  Image of the house with measurements

Next, she went to the local hardware store and learned that there are many different types of paint. So she created a table to compare the different kinds and determine which would be best.

Assignment

1. Calculate the square area of the side of the house. Image of the house with measurements.
2. Create your own table comparing the prices of paint. Choose three types of paint. Some might contain primer, a substance that helps the paint stick better and appear darker. These are often more expensive, but that would be one less coat of paint. You can use this sample table or make your own. 
3. Summarize the plan of action that Sally should take.

Price/Gallon Coverage Surface area of #Gallon of Number of Total # of Cost

side of house coat coats gallons

Type of paint
Behr		200-400
Sherwin Williams		350
Glidden (no primer)		350
Primer		350

Answer 1

Your triangle is 27.2°, 27.2°, 125.6°, 35ft.

Lets get the height. a/sinα=b/sinβ=c.

a/sin27.2=17.5/sin62.8=19.675......=c

a=8.993....

a*b=8.993*17.5=157.391.....sq/ft

+350

=507.4sq/ft