Download Right Triangle Trigonometry Day 1

1
Right Triangle Trigonometry
Trigonometry is based upon ratios of the sides of right
triangles.
The ratio of sides in triangles with the same angles is
consistent. The size of the triangle does not matter
because the triangles are similar (same shape different
size).
2
The six trigonometric functions of a right triangle,
with an acute angle , are defined by ratios of two sides
of the triangle.
hyp
opp
The sides of the right triangle are:
 the side opposite the acute angle ,
 the side adjacent to the acute angle ,
 and the hypotenuse of the right triangle.
θ
adj
3
hyp
The trigonometric functions are
opp
θ
adj
sine, cosine, tangent, cotangent, secant, and cosecant.
opp
sin  =
cos  = adj
tan  = opp
hyp
hyp
adj
csc  =
hyp
opp
sec  = hyp
adj
cot  = adj
opp
Note: sine and cosecant are reciprocals, cosine and secant are reciprocals,
and tangent and cotangent are reciprocals.
4
Reciprocal Functions
Another way to look at it…
sin  = 1/csc 
cos  = 1/sec 
tan  = 1/cot 
csc  = 1/sin 
sec  = 1/cos 
cot  = 1/tan 
5
Given 2 sides of a right triangle you should be able to find
the value of all 6 trigonometric functions.
Example:
5

12
1
What if I tell you that cos 𝜃 = ; can you find the other 5
5
trigonometric ratios?
Standard Triangle with A, B, C, a, b, and c
Angles: capital letters (A, B, and C) or greek letters (θ, α)
Sides: lower case letters (a, b, c)
Same letters are opposite of each other.
A
b
c
C
B
a
Solve for all missing sides and angles if b = 5 and c = 10.
Assume C is the right angle.
1st: Draw the triangle
2nd:Pick an angle to use as a reference
3rd: Label opposite, adjacent, and hypotenuse
4th: Start solving!
You are 330 feet from the base of a building. The angles of
elevation to the top and bottom of a flagpole on top of the
building are 55o and 53o. Find the height of the flag pole.
1st: Draw the picture
2nd: Solve for each triangle
3rd: Answer the question
• Exit slip time!
• Homework: Day 3 on assignment guide!
• (I have the dates wrong!)
• Quiz coming up on Friday
• (this is a change from the assignment guide)