Download Notice that we have added three new ratios.

CP Algebra II
Name: ________________________
11-1 Trig Functions in Right Triangles
4/17/14
Warm-Up #1:
Use your protractor and ruler to make the following measurements.
mA 
AC 
mB 
AB 
mC 
CB 
Calculate each ratio:
CB

AC
AB

AC
CB

AB
Warm-Up #2:
Use your protractor and ruler to make the following measurements.
mM 
MP 
mN 
MN 
mP 
PN 
Calculate each ratio:
PN

MP
MN

MP
PN

MN
Warm-Up #3:
Use your protractor and ruler to make the following measurements.
mR 
RT 
mS 
RS 
mT 
TS 
Calculate each ratio:
TS

RT
RS

RT
TS

RS
CP Algebra II
Name: ________________________
11-1 Trig Functions in Right Triangles
4/17/14
Use the people around you to fill in all the values
CB
AB


AC
AC
CB

AB
PN

MP
MN

MP
PN

MN
TS

RT
RS

RT
TS

RS
1. What are some patterns that you notice about the ratio of the sides of the triangle?
2. No matter how big or small the triangle is, the ratio of the side opposite to the 27 angle to the
hypotenuse is
.
3. No matter how big or small the triangle is, the ratio of the side adjacent to the 27 angle to the
hypotenuse is
.
4. No matter how big or small the triangle is, the ratio of the opposite side to the adjacent side of the 27
angle is
.
-----------------------------------------------------------------------------------------------------------Conclusion: Trigonometric ratios in right triangles are dependent only on the ______________________,
not on the ______________________ !
Remember… S

o a o
C T
h h a
Notice that we have added three new ratios.
Example #1: Find the six trigonometric values in the right triangle for  :

Example #2: Find the six trigonometric values in the right triangle for  :

Example #3: Use a trigonometric function to solve for x. Round to the nearest tenth.
Example #4: Use a trigonometric function to solve for x.
Example #5: Use a trigonometric function to solve for  . How is this different than solving for a side?

Solving for angles in right triangles...
Example #6: Solve for the indicated angle.
Angle of Elevation
vs.
Angle of Depression
Example #7: An observer in the Cape May Lighthouse spots a ship in the ocean. The angle of depression from
the observer to the ship is 13˚. The observer is 157 feet above the sea level. How far is the boat from the base of
the lighthouse?
Example #8: A golfer is standing at the tee, looking up to the green on a hill. If the tee is 36 yards lower than
the green and the angle of elevation from the tee to the hole is 12˚, find the distance from the tee to the hole.
Example #9: A ramp for unloading a moving truck has an angle of elevation of 32˚. If the top of the ramp is 4
feet above the ground, what is the length of the ramp?
Example #10: A square has a diagonal of length one foot. What are the dimensions of the square? Label all
angles.
Example #11: An equilateral triangle has side lengths of one foot. An altitude is drawn from the top vertex to
the base of the triangle, cutting the base in half. The sides are each one unit. Draw a picture and determine the
length of the altitude. Then, label all angles.