Lets Apply: Architecture!

The Unit Circle has a lot of real life applications. Sine, Cosine and Tangent are used frequently in construction.


     Surveyors need to know the height of a building in order to build buildings nearby with the same height measure. (This way, the buildings don't look awkward when they are built next to each other!)
There is a very simple way to figure this out:
First, the surveyor needs to stand a certain distance from the side of the building they want to find the height of. The surveyor should then , measure that distance in the units they want to find the height of the building in.
From the point where the surveyor is standing, draw an imaginary line upward, and using surveying tools, you can figure out that measure (called measure of elevation).
Then, use tangent and the measure of elevation, or theta. to find the height of the building:
     Tangent(theta)=A/B

Multiply the B out on both sides:
    Btangent(theta)=A


     To complete a roof, constructors need to know how long the roof is to know how long the boards that will cover the roof will be. (That way, your house will have even boards that cover the roof!)
There is a very simple way to figure this out:
First, the constructor needs to know the angle at the top of the roof...divided by two. We will call this angle theta. Also, the constructor needs to know either half the length of the base of the roof OR the height of the roof.
Then, use sine or cosine (depending on what given information you have to solve the length of the top of the roof.

     If you know the height of the roof:

Cos(theta)=h/length of roof  and multiply the length of roof on both sides:

length of roof(cos)theta=h  remember we're solving for the length of roof...divide both sides by cos(theta):

length of roof=h/cos(theta)

If you know the half the base of the roof (b):

sin(theta)=b/length of roof  and multiply the length of roof on both sides:

length of roof(sin)theta=b  remember we're solving for the lenght of roof...divide both sides by sin(theta):

length of roof=b/sin(theta)

Remember that there is a way to find sine, cosine and tangent measures of 30-60-90 and 45-45-90 triangles easily! (This "trick" is how we plot points on the unit circle!) You can apply this to get exact measurements when constructing, to get the most accurate results possible.)