Algebra 2 Trig Problem

Question

I really only need the area of the side of the house explained, I'm stuck and don't know how to do it. Here's the problem:

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. Summarize the plan of action that Sally should take.

Answer 1

The side angle=117.2 - 90=27.2 Degree

The top angle: 180 - 2(27.2)=125.6 Degree

sin(125.6)/35=sin (27.2)/a

a=19.68 ft

h²=a²-(35/2)²

h=8.994 ft

A_Tri=35x 8.994/2=157.39 ft²

A_Squ=10x 35=350 ft²

Total Area=157.39+350=507.39 ft²

Answer 2

Here are some hints to get you started, based on the numbered directions given in the diagram.

1) This step has already been completed, dividing the side of the house into a rectangle and an isosceles triangle. The area of the rectangle is easy.

2) The angle you are asked to calculate is 117.2 - 90. Since it is an isosceles triangle its base angles are equal.

3) Since 3 angles of a triangle add to 180, the vertex angle must be 180 - the sum of the two base angles.

4) Sine of vertex angle is to long side of rectangle as leg of isosceles triangle in the sine of the angle you calculated in step 2.

5) The formula for the area of a triangle when you know two sides and the included angle is

A = 1/2 a b sin θ where a and b in this case are the legs of the triangle and theta is the vertex angle.

6) Add the area of the triangle to the area of the rectangle to get area of the side of the house.