Transcript Geometry Notes

Geometry Notes
Lesson 5.3C Trigonometry
T.2.G.6 Use trigonometric ratios (sine, cosine,
tangent) to determine lengths of sides and
measures of angles in right triangles including
angles of elevation and angles of depression
T.2.G.7 Use similarity of right triangles to
express the sine, cosine, and tangent of an
angle in a right triangle as a ratio of given
lengths of sides
Solving for unknown values
Steps:
1. Label the sides as: opposite, adjacent,
hypotenuse.
2.
Decide which trig ratio is needed:
(sine, cosine, or tangent).
3.
Set up Equation
4.
Use Calculator to Solve.
We Will Work Backwards
• Since we know the ratio of the sides for
every _______________, then we can
find any angle, given 2 ___________of a
right triangle.
Example #1
Find x. Round your answer to the
nearest tenth.
39
x
18
Example #2
Find x. Round your answer to the
nearest tenth.
15
x
11
Now You Try…
Find x. Round your answer to the
nearest tenth.
18.3
x
41.7
Angle of
Elevation/Depression
• Angle of Elevation:
When a point is viewed from a lower point, the angle that
person’s line of sight makes with the horizontal
• Angle of Depression:
An angle that mopes around the house all day saying “I
hate my life, nobody likes me.”
JUST KIDDING!
When a point is viewed from a higher point, the angle that
person’s line of sight makes with the horizontal
Illustrations
Example #4
If state law requires playground slides
to be placed at a 30o angle of
elevation and the slide is 10 feet
long, how many feet are needed on
the playground for the slide?
Steps
If state law requires playground slides to be placed at a 30o
angle of elevation and the slide is 10 feet long, how
many feet are needed on the playground for the slide?
1.
Draw a picture
2.
Label the sides as opposite, adjacent, hypotenuse
3.
Decide which Trig ratio is needed:
(Sine, Cosine, Tangent)
4.
Set up Equation
5.
Use Calculator to solve.
Now You Try…
A guy wire is attached to the top of a
telephone pole. Its angle of
depression with the horizontal is 76o.
If the pole is 20 feet tall, how long is
the wire?