05-12-2012, 12:25 PM
TRIGONOMETRY
1TRIGONOMETRY.ppt (Size: 941 KB / Downloads: 48)
But what if you want to know the angles?
Well, here is the central insight of trigonometry:
If you multiply all the sides of a right triangle by the same number (k), you get a triangle that is a different size, but which has the same angles:
How does that help us?
Take a triangle where angle b is 60º and angle a is 30º
If side B is 1unit long, then side C must be 2 units long, so that we know that for a triangle of this shape the ratio of side B to C is 1:2
There are ratios for every
shape of triangle!
But there are three pairs of sides possible!
Yes, so there are three sets of ratios for any triangle
They are mysteriously named:
sin…short for sine
cos…short for cosine
tan…short or tangent
and the ratios are already calculated, you just need to use them
Some terminology:
Before we can use the ratios we need to get a few terms straight
The hypotenuse (hyp) is the longest side of the triangle – it never changes
The opposite (opp) is the side directly across from the angle you are considering
The adjacent (adj) is the side right beside the angle you are considering
Why do we need the sin & cos?
We use sin and cos when we need to work with the hypotenuse
if you noticed, the tan formula does not have the hypotenuse in it.
so we need different formulas to do this work
sin and cos are the ones!
Here is an example
Spike wants to ride down a steel beam
The beam is 5m long and is leaning against a tree at an angle of 65° to the ground
His friends want to find out how high up in the air he is when he starts so they can put add it to the doctors report at the hospital
How high up is he?
Two Triangle Problems
Although there are two triangles, you only need to solve one at a time
The big thing is to analyze the system to understand what you are being given
Consider the following problem:
You are standing on the roof of one building looking at another building, and need to find the height of both buildings.