as a matter of fact, right triangles end up being more of a rarity than commonplace
DESCRIPTION
There is no doubt that the 3 PTRs are extremely useful when solving problems modeled on a right triangle. Unfortunately, the world does not consist only of right triangles…. As a matter of fact, right triangles end up being more of a rarity than commonplace. - PowerPoint PPT PresentationTRANSCRIPT
There is no doubt that the 3 PTRs are extremely useful when solving problems modeled on a right triangle.
Unfortunately, the world does not consist only of right triangles…
Does that mean when we come across a situation that can only be modeled with a non-right triangle that we abandon our pursuit?….
No Way!!!!There exists two Laws of
Trigonometry that allow one to solve problems that involve non-right Triangles:
RememberA capital letter represents an
angle in a triangle, and a small letter represents a side of a
triangle
A
a
A BO
C
b
c
a
If b,c and O are all known, then O is called a “Contained Angle”
(the blue line also forms a “c”, [kind of] which is how I remember to use the “c”osine law in this case..)
A BO
C
b
c
a
The Cosine Law can be used to find the length of the opposite side to O
In this case, the length of side a
a2 = 82 + 102 – 2(8)(10)Cos50o
A50o
C
8m
10m
a
a2 = 61.15m a = 7.8 m
B
a2 = b2 + c2 – 2(b)(c)CosAo
You should be able to load this into your calculator directly from left to right…if not, see me
The Sine Law
If the triangle being solved does not consists of a right triangle (3PTRs) or a contained angle (Cosine Law), then another tool must be used.
The Sine Law can be used to determine an unknown side or angle given an “opposing pair”
A
C
Bc
b a
O1 O2
Find the length of a
a
A
C
c
2473o
57o
N
We can not use the Cosine Law because there is not a contained angle…
We must therefore look for an opposite pair. Hmmm…..
A-HA!!!(it’s all good)
Find the length of a
a
A
C
c
24
57o
N
aSin73o
= 24Sin57o
a = 27.4
73o
Again, this can be put directly into your calculator. See me for help.