2. Trigonometric ratios are used with
right triangles to solve for missing
angles and/or sides.
The 3 main trig ratios are:
Sine
Cosine
Tangent
3. Sides are labeled in reference to a
designated angle, θ (“theta”)
Hypotenuse: the longest side. Always
opposite the right angle.
Adjacent: side that is
touching the angle θ.
Opposite: side across
from the angle θ.
4. name ratio notation
sine opp/hyp sin(θ)
cosine adj/hyp cos(θ)
tangent opp/adj tan(θ)
5. Set up the ratio using the
correct side lengths.
Reduce if possible.
OR – divide and round your
answer.
Depends on the directions given.
6. Find the value of each trig ratio.
sin A=
cos A=
tan A=
sin B=
cos B=
tan B=
7. Find the value of each trig ratio to
the nearest ten-thousandth.
sin R=
cos R=
tan S=
8. Inverse trig ratios are used to solve
for missing angle measures.
They include:
sin-1
cos-1
tan-1
On your calculator: hit “2nd” and
then the trig button you need
9. When given a decimal value:
Find each angle measure to the
nearest degree.
sinθ = 0.7193
cosθ = 0.3907
tanθ = 0.6009
10. When given a triangle:
Set up the appropriate ratio,
then use the inverse.
Find the measure of the indicated
angle to the nearest degree.
22. A 30-60-90 is half of an equilateral
triangle.
That means the hypotenuse is twice
the short leg.
We can use the Pythagorean
Theorem to find the long leg.
23. It follows that for any 30-60-90,
the same relationships are true.
In general:
60º
24. Find
the missing side lengths. Leave
answers in simplest radical form.
31. Remember: A = ½bh for triangles
Use trig to find the length of the
base and height.
Then find the area.
Example:
32. Hints for successful problem solving:
Draw a picture!
Label all given information.
Mark the angles or sides you need to find.
Use a different variable for each quantity.
Create a game plan!
Solve using trig.
Check that your answer is reasonable.
The hypotenuse is always the longest
side!
33. Angle of elevation – measured
upward from the horizontal.
Angle of depression – measured
downward from the horizontal.
34. A light house is 60 meters high with its
base at sea level. From the top of the
lighthouse, the angle of depression of a
boat is 15 degrees.
A. How far is the boat from the foot of
the light house?
B. How far is the boat from the top of
the lighthouse?
35. Katieand Sara are attending a theater
performance. From her seat, Katie looks
down at an angle of 18 degrees to see
the orchestra pit. Sara's seat is in the
balcony directly above Katie. Sara looks
down at an angle of 42 degrees to see
the pit. The horizontal distance from
Katie's seat to the pit is 46 ft. What is
the vertical distance between Katie's
seat and Sara's seat?