Right Triangle Trigonometry

1
Section 4.3

• Right Triangle Trigonometry

2
Overview

• In this section we apply the definitions of the
  six trigonometric functions to right triangles.
• Before we do that, however, lets remind
  ourselves about the Pythagorean Theorem

3
A Picture
4
SOH-CAH-TOA
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An Example
State the six trigonometric values for angles C
and T.
6
Complimentary Angles

• In a right triangle, the two acute angles are
  complimentarythat 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

7
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).

8
Special Right Triangles

• One special right triangle, the 30-60-90, is
  formed from an equilateral triangle with sides of
  1 unit

9
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

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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).

11
Examples