INTRODUCTION TO ENGINEERING TECHNOLOGY

SEVENTH EDITION ROBERT J. POND & JEFFERY L. RANKINEN CHAPTER 6 RIGHT-TRIANGLE TRIGONOMETRY AND GEOMETRY FOR TECHNOLOGISTS

RIGHT-TRIANGLE RELATIONSHIPS

• THE 3-4-5 TRIANGLE HAS LEGS MEASURING 3 AND 4 UNITS AND THE HYPOTENUSE MEASURING 5 UNITS • • IT IS A RIGHT TRIANGLE SOMETIMES CALLED THE “MAGIC 3-4-5 TRIANGLE” a B b c A Sides are named with lower case letters; such as a, b, c Think of a as altitude and b as base. c is the hypotenuse.

Angles are identified by capital letters and are opposite the sides with the same letter.

• • •

RIGHT-TRIANGLE RELATIONSHIPS

Carpenters still use 3-4-5 Triangle When the sides of a right triangle are all integers, it is called a Pythagorean Triple PYTHAGOREAN THEOREM ►

c

2 

a

2 

b

2 Three angles always total 180º ► ► For a right triangle, angles A and B total 90º 2 angles that add to 90º are called complementary

TRIGONOMETRIC FUNCTIONS

“sohcahtoa” sin   opposite side hyponenuse = a _ c B cos   adjacent side hyponenuse c a tan   opposite side adjacent side A  b 90 o Inverse Trig functions are used to find angle measurements when you know the sin, cos, or tan. They are written as, for example, inv sin or sin and cotangent.

-1 They are not the same as reciprocal functions known as the secant, cosecant,

OTHER TRIGONOMETRIC FUNCTIONS

• INVERSE FUNCTIONS, SUCH AS TAN -1 , SIN -1 , AND COS -1 , WILL GIVE THE ANGLE VALUE, WHEN THE FUNCTION VALUE IS KNOW. THESE ARE ALSO CALLED ARC TANGENT, ARC SINE, AND ARC COSINE. • THE COS -1 (0.500) = 30 o • THE COSECANT, SECANT, AND COTANGENT FUNCTIONS ARE RECIPROCALS OF THE SINE, COSINE AND TANGENT FUNCTIONS • =

HYPOTENUSE OPPOSITE SIDE

=

HYPOTENUSE ADJACENT SIDE

=

ADJACENT SIDE OPPOSITE SIDE

TRIG EXAMPLE

• FIND THE TOTAL IMPEDANCE, Z T , AND THE ANGLE, Θ, OF THE AC CIRCUIT BELOW.

Tan A = opp = -3/4= - 0.75

adj Use inv Tan or Tan of – 36.87

o -1 to find angle measurement To find Z Pythagorean Theorem a 2 + b 2 T , Use the = c 2 2 4 2 + (-3) = c 2 16 + 9 = 25 √25 = c 2 5 = c = Z T