Transcript File - We Mean Business.

Warm up: Pythagorean Theorem
Review
1. What is it?
1. When do we use it?
1. Why is it important?
Can we use the Pythagorean Theorem
to find x?
x
10
52°
Trigonometry!!!
• From Greek:
• Trigo = Triangle
• Metr = measure
• So it means MEASURING TRIANGLES!!
38
Which SIDES is adjacent?
Opposite?
The hypotenuse?
52
leg
B
A
leg
C
Hypotenuse = side opposite right angle
Opposite side = the leg that’s farthest away and
not touching the angle
Adjacent side = the leg that is closest to the angle
Trigonometric Ratio
• A trigonometric ratio or a ratio of the lengths
of two sides of a right triangle.
• There are three basic trig ratios we will be
looking at today: sine, cosine, and tangent.
Trigonometry Ratios
KEY CONCEPT:
RATIO
SINE
TRIG RATIOS
WORDS
sin = opposite
hypotenuse
SYMBOLS
MODELS
Sin A = 4
5
5
A
4
3
COSINE
cos = adjacent
hypotenuse
cosA = 3
5
5
4
A
3
TANGENT
tan= opposite
adjacent
tanA= 4
3
5
4
A
3
Shortcut!
• SOH CAH TOA is a suuuuper way to remember
the trig ratios!
Sin
Opposite
Hypotenuse
Cos
Adjacent
Hypotenuse
Tangent
Opposite
Adjacent
Express each ratio as a fraction and as
a decimal (hundredths place)
a) sin A
b) cos A
c) tan A
d) sin B
e) cos B
NOT ON WORKSHEET
f) tan B
On your own!
a) sin A
b) cos A
c) tan A
d) sin B
e) cos B
f) tan B
Warm Up
Use Pythagorean theorem to solve for the missing side then set
up each ration
a) sin A
A
b) cos A
c) tan A
d) sin B
B
e) cos B
f) tan B
C
On your calculator: Press the sin, cos
or tan button, enter the angle
measure, close the parentheses and
hit
enter
• sin30 =
• cos45 =
• tan78 =
• cos50 =
• tan37 =
• sin50 =
You must first make sure that your calculator is
in degree mode
PAY CLOSE ATTENTION!!!
Finding a missing side using trig
• Solve for the indicated side.
Steps
1)
2)
3)
4)
5)
Choose a reference angle
Label the sides
Choose the correct ratio
Setup the equation
Solve
Find x
3
x
60°
Find x.
30
°
x
5
On your own!
x
32°
18
Here’s the tricky part: how can we
do this backwards?
3
4
x°
Use the inverse functions on your
calculator!
• SIN-1
• COS-1
• TAN-1
Find x (round to the ones place):
1)sinx= .75
2)cosx = .80
3)tanx = .54
x°
Find x. Round to the nearest tenth.
Solve for x. Round to the nearest
tenth.
On your own
Do Now
Today we’re learning some new terms: Angle of
depression and Angle of Elevation.
a.) What do you think angle of depression is?
b.) What do you think angle of elevation is?
TRIG IN THE REAL WORLD!!
Trig can be used in real life!
• To talk about trig in the real world, you need
to know a few definitions:
• ANGLE OF ELEVATION: The angle between the
upward line of sight to an object and the
horizon .
angle of elevation
• Tyrell went to the fair and saw a cute girl
on the ferris wheel. He was like, “Oh
snap! Shawty right there is a ten! I
wonder how high up she is!” So he used
his protractor (that he always carries
with him) to find the angle of elevation
and found that it was 47°. If he was
standing 20 feet from the ferris wheel,
what was its height?
On your own: Brionna was out on Lake Gaston on a boat
with her cousins and they saw a high cliff and thought
it would be fun to jump off it into the water. but
Brionna was like, “Wait, let’s figure out it’s height
first.” So they found the angle of elevation to be 39°.
And they measured that they were 50 ft from the cliff.
Should they jump off?
A roofer props a ladder against a wall so
that the top of the ladder reaches a 30foot roof that needs repair. If the angle of
elevation from the bottom of the ladder to
the roof is 55°, how far is the ladder from
the base of the wall? Round your answer
to the nearest foot.
ON YOUR OWN Suppose the sun casts a
shadow off a 35-foot building. If the angle
of elevation to the top of the building is
60°, how long is the shadow to the
nearest tenth of a foot?
angle of depression
• ANGLE OF DEPRESSION: The angle
between the downward line of sight to
an object and the horizon.
• The angle of depression is always
congruent to the angle of elevation.
angle of depression
angle of depression
?
35°
50 ft
angle of depression
22°
?
82 ft
Kyle is at the end of a pier 30 feet above
the ocean. His eye level is 3 feet above the
pier. He is using binoculars to watch a
whale surface. If the angle of depression
of the whale is 20°, how far is the whale
from Kyle’s binoculars?
 1. The angle of elevation from the base to the
top of a waterslide is about 28˚. The slide
extends horizontally about 45.8 meters.
Estimate the height h of the slide.
 2. An 18-foot ladder is leaning against a wall.
The foot of the ladder is 6 feet from the base of
the wall. What is the approximate measure of
the angle the ladder forms with the ground?
 3. The control tower views a plane landing at a
19° angle of depression, as show. How far is the
plane from the base of the control tower?
114 ft.