Transcript right triangle

Right Triangle Trigonometry
Day 1
Pythagorean Theorem
• Recall that a right triangle has a 90° angle as one of its
angles.
• The side that is opposite the 90° angle is called the
hypotenuse.
• The Pythagoreans theorem says that the square of the
hypotenuse is equal to the sum of the squares of the
legs.
c2 = a2 + b2
a
c
b
Similar Triangles
•
•
Triangles are similar if two conditions are met:
1. The corresponding angle measures are equal.
2. Corresponding sides must be proportional. (That is, their
ratios must be equal.)
The triangles below are similar. They have the same shape,
but their size is different.
a b c
 
d e f
A
D
c
b
f
E
B
a
C
e
d
F
Example
• Find the missing side lengths for the
similar triangles.
3.2
3.8
x = (54.4)(3.8)/3.2 = 64.6
y = (42.5)(3.2)/54.4 = 2.5
y
54.4
x
42.5
Introduction to Trigonometry
opp is the side opposite angle A
• adj is the side adjacent to angle A
• hyp is the hypotenuse of the right triangle
hyp
opp
adj
A
Define the three basic trigonometric ratios:
sine, cosine and tangent.
Just remember
sohcahtoa!
Sin Opp Hyp Cos Adj Hyp
Tan Opp Adj
-or-
Opp
Sin ( A) 
Hyp
Adj
Cos ( A) 
Hyp
Opp
Tan( A) 
Adj
During a trip to Italy,
you visited a wonder of
the world, the Leaning
Tower of Pisa. Your
guidebook explains
that the tower now
makes an 85 degree
angle with the ground
and measures 179 feet
in height. If you drop a
stone straight down
from the top of the
tower, how far from the
base will it land?
Two acute angles are complementary if their sum is
a right angle.


are complimentary angles
c
b

a
and 
Cofunctions of complimentary angles are
equal

c
b

a
b
sin    cos 
c
a
cos    sin 
c
Cofunctions of complimentary angles are
equal
sin   cos(90   )

cos   sin( 90   )

h
25

70
h = 23.49
*This time use the equivalent cofunction.
h
25

70
h
cos(90  70) 
25
h
cos( 20) 
25
25 cos( 20)  h
h = 23.49