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 D

c b f e

E d F B a C

f

c

e

b

d

a

Example

• Find the missing side lengths for the similar triangles.

3.2 3.8

y

54.4 x

42.5

x = (54.4)(3.8)/3.2 = 64.6

y = (42.5)(3.2)/54.4 = 2.5

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-

dj

ppAan

yp

djAos

yp

ppAin

A

OT

H

AC

H

OS

)(

)(

)(

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.

a

b

c

and

are complimentary angles

b

c

sincos

cossin

c

ac

b

Cofunctions of complimentary angles are equal

a

)90sin(cos

)90cos(sin

Cofunctions of complimentary angles are equal

25

70

h

h = 23.49

25

70

h

h = 23.49

25)7090cos(

h

25)20cos(

h

h)20cos(25

*This time use the equivalent cofunction.