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 sin  

opp hyp

cos  

adj hyp

tan  

opp adj

csc  

hyp opp

sec  

hyp adj

cot  

adj 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