Transcript Slide 1

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”
B
a
b
Sides are named with lower case letters; such as a, b, c
Think of a as altitude and b as base. c is the
c
hypotenuse.
Angles are identified by capital letters and are
A
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  a b
2
2
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”
oppositeside
sin  
hyponenuse
adjacent side
cos 
hyponenuse
oppositeside
tan 
adjacent side
= a_
c
=
B
c
b_
c
= a_
b
a
A
90o

b
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-1
They are not the same as reciprocal functions known as the secant, cosecant,
and cotangent.
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) = 30o
• 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, ZT, AND THE ANGLE, Θ, OF THE AC CIRCUIT BELOW.
Tan A = opp = -3/4= - 0.75
adj
Use inv Tan or Tan-1
to find angle measurement
of – 36.87o
To find ZT , Use the
Pythagorean Theorem
a2 + b2 = c2
42 + (-3) 2 = c2
16 + 9 = 25
√25 = c2
5 = c = ZT