Download Geometry Lesson 7-4

GEOMETRY
LESSON 7-4
TRIGONOMETRY
Pg. 364-370
Objectives:
1. Find trigonometric ratios using right triangles
2. Solve problems using trigonometric ratios.
KEY CONCEPT: Trig can be used to solve a plethora of missing angles and/or sides involving right
triangles
Terms:
1. Trigonometry: means triangle measure (relation of side measures and associated angles)
2. Adjacent Leg: Triangle leg physically touching the indicated angle
3. Opposite Leg: Triangle leg across the triangle from the indicated angle
4. Hypotenuse: The longest side of the triangle directly across from the right angle
5. Theta (Ө): The indicated angle for reference with the trig functions (one of the two acute angles)
B
This Right Triangle is the basis for the following:
Opposite
Leg
Hypotenuse
Ө
C
Adjacent Leg
1. Sine of Angle A  sin A = opposite = opp = BC
hypotenuse hyp BA
2. Cosine of Angle A  cos A = adjacent = adj = CA
hypotenuse hyp BA
A
3. Tangent of Angle A  tan A = opposite = opp = BC
Adjacent adj
CA
REMEMBER THIS MNEMONICS: “SOH-CAH-TOA”
Meaning…
Sine is Opposite over Hypotenuse--Cosine is Adjacent over Hypotenuse – Tangent is Opposite over
Adjacent
NOTE: You can use the same concepts for Angle B, but the opposite and adjacent switch locations
To calculate the measure of Angle A or B, use a calculator with trig functions using the arc sine or arc
cosine or arc tan function keys (sin-1 cos-1 tan-1) These are known as the “inverse functions”
NOTE: Be sure the calculator “Mode” is in “degrees” not “radian”
EXAMPLE 1
If you know the leg measures:
Sin A = opp/hyp = 5/10
EXAMPLE 2
If you know a side and an angle:
Angle A = 7 degrees; Hypotenuse is 5
sin-1 (5/10) = A
30 degrees = A
sin (7) = opp/5
5(sin(7)) = opp
0.609 = opposite leg