Transcript Section 4.3 - Shelton State Community College

Section 4.3
Right Triangle Trigonometry
Overview
• In this section we apply the definitions of the six
trigonometric functions to right triangles.
• Before we do that, however, let’s remind
ourselves about the Pythagorean Theorem:
A Picture
SOH-CAH-TOA
opp
sin  
hyp
adj
cos 
hyp
opp
t an 
adj
hyp
csc 
opp
hyp
sec 
adj
adj
cot 
opp
An Example
State the six trigonometric
values for angles C and T.
Complimentary Angles
• In a right triangle, the two acute angles are
complimentary—that is, their angle
measures add up to equal 90 degrees.
• Complimentary angles in a right triangle
have special relationships in terms of their
trigonometric values:
Cofunctions
• The sine of an angle is equal to the cosine
of its compliment (and vice versa).
• The tangent of an angle is equal to the
cotangent of its compliment (and vice
versa).
• The secant of an angle is equal to the
cosecant of its compliment (and vice
versa).
Special Right Triangles
• One special right triangle, the 30-60-90, is
formed from an equilateral triangle with
sides of 1 unit:
Special Right Triangles,
continued
• Another right triangle, the 45-45-90, is
formed by drawing a diagonal in a square
with sides of 1 unit:
Solving Right Triangles
1. Write the appropriate trigonometric
relationship for the unknown value (there
may be more than one).
2. Use your scientific calculator to find the
appropriate trigonometric value or angle
(make sure your calculator is in degree
mode).
Examples