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Introduction to
Trigonometry
Unit IIC Day 3
Do Now
 Geometry Review: The Angle-Angle Similarity Theorem
states that if two triangles have two pairs of congruent
angles, then the triangles are similar.
 Are the following triangles similar? If so, how would you
prove it?
Trigonometry
 Trigonometry is the study of ratios of sides in right
triangles.
 We refer to sides in relation to a given angle as
opposite the angle, adjacent to the angle, or as the
hypotenuse.
Ex. 1: Identifying Side
Lengths
a) If you are “standing” at vertex D, which side is the
hypotenuse? Which is the opposite side? Which is the
adjacent side?
b) If you are “standing” at vertex E, which side is the
hypotenuse? Which is the opposite side? Which is the
adjacent side?
Note on Sides
 We never “stand” at the right angle.
 The hypotenuse is the hypotenuse; it is never
considered adjacent even though it might appear to be.
Ex. 2: Ratios
 “Standing” at vertex G, what is the ratio of the opposite
side to the adjacent side?
 What does this ratio represent?
Ex. 2A: Ratios
 “Standing” at vertex B, what is the ratio of the opposite
side to the adjacent side?
 What does this ratio represent?
Ex. 3: Comparing Ratios
a) Standing at angle A, what is the ratio of the opposite side to the
adjacent side?
b) Standing at angle D, what is the ratio of the opposite side to the
adjacent side?
c) Standing at angle G, what is the ratio of the opposite side to the
adjacent side?
 What can we conclude about the ratio of the opposite to the
adjacent anytime we are standing at the 45 angle of any right
triangle?
The Tangent Function
 The tangent of an angle in a right triangle is the ratio of
the opposite side length to the adjacent side length.
 We can think of tangent as a function that takes an
angle measure as its input and gives the ratio
opposite/adjacent as its output.
Angle (º)
Opp./Adj.
15º
30º
45º
60º
Ex. 4: Finding Tangent
a) Find the tangent of R.
a) Find the tangent of S.
Six Trigonometric Ratios
 There are six trig. ratios:
 sine, cosine, tangent
 cosecant, secant, and cotangent
Ex. 5
 Find the six trigonometric ratios for R in the triangle
above.