Download Section 10.6 – Right Triangle Trig

Chapter 10. Section 6
Page 1
Section 10.6 – Right Triangle Trig
Homework (pg 557) 1-40
•
Definition: Trigonometry is the study of the relationship between right triangles angles and sides
•
We must first be able to identify the parts of a triangle, no matter what position it is in the labels
remain the same
•
The three fundamental trig functions are
sin (θ) = opposite / hypotenuse
cos (θ) = adjacent / hypotenuse
tan (θ) = sin (θ) / cos (θ) = opposite / adjacent
•
Given any two sides of a right triangle, you can find the third side and find the trig values for any
angle
Example (Checkpoint 1): Find sine, cosine and tan of θ in the figure
Solution: The missing side =
sin(θ) = 3/5
cos(θ) = 4/5
tan(θ) = ¾
32 + 42 = 5
•
Given any side of a right triangle and any angle (other than 90) you can find all other angles and all
other sides
Example (Checkpoint 2): Find all pieces of the triangle given
Solution:
θ = 180 – 90 – 40 = 50
a
tan40 =
⇒ a = 150(tan40) = 125.86
150
c = 125.862 + 1502 = 195.81
•
Many application problems use angle of elevation which is the angle made up from the horizontal
line of sight, or angle of depression which is the angle made down from the horizontal line of sight