TRIGONOMETRY
Objective:
To use the sine, cosine, and
tangent ratios to determine
missing side lengths in a
right triangle.
RISE AND SHINE, MATHLETES!
AGENDA
HOMEWORK
1. HOMEWORK CHECK
FINISH TRIG WORKSHEET
2. NOTES – INTRO TO TRIG
3. PRACTICE
WHAT IS “TRIGONOMETRY”?
Trigonometry deals with triangles.
The word trigonometry actually comes from the Greek words trigon
meaning—no big surprise here—triangle, and metron meaning
something like “measure.”
Trigonometry is all about figuring out clever ways to measure and
calculate the properties of the components of triangles—namely their
three sides and three angles.
IN A RIGHT TRIANGLE…
There are ratios we can use to determine side lengths. These ratios are
constant, no matter what the lengths for the sides of the triangle are.
These ratios are called trigonometric ratios.
Three of the trigonometric ratios are:
Sine (sin)
Cosine (cos)
Tangent (tan)
SOHCAHTOA
TRIG RATIOS
=
=
=
leg opposite of angle
hypotenuse
leg adjacent to angle
hypotenuse
opposite leg
adjacent leg
1. WRITE THE TRIG RATIO FOR THE FOLLOWING:
2. USE THE TRIANGLE TO WRITE EACH TRIG
RATIO.
HAVING TROUBLE WITH DECIDING WHAT IS
“OPPOSITE” VS. “ADJACENT?
3. USE THE TRIANGLE TO WRITE EACH TRIG RATIO
IF GIVEN THE ANGLE MEASURE, YOU CAN USE A TRIG
FUNCTION TO FIND A MISSING SIDE LENGTH OF A RIGHT
TRIANGLE
Which trig ratio relates the given
angle, and the 2 sides?
Set up equation:
5. FIND X.
6. FIND X.
WORD PROBLEMS
Draw a picture.
Draw a picture.
Draw a picture.
7. To measure the height of a tree, Noah walked
125 ft. from the tree, and measured a 32˚angle
from the ground to the top of the tree. Estimate
the height of the tree.
WORD PROBLEMS
Draw a picture.
Draw a picture.
Draw a picture.
8. A 20 ft wire supporting a flagpole forms a 35˚
angle with the flagpole. To the nearest foot, how
high is the flagpole?