Transcript Right Triangle Trigonometry

Warm Up
Find the missing sides of the following triangles:
7
15
8
3
Answers
Find the missing sides of the following triangles:
17
15
7
3
7.62
8
Trigonometry
Trigonometry was developed by
Greek mathematicians over
2000 years ago. It was created
to study astronomy. By
understanding the relationships
between sides and angles,
astronomers could map the
movements of planets and
stars.
First, we will focus on right triangles!
Today, you will learn how to:
• solve for a missing side of a right triangle
• solve for a missing angle of a right triangle
Later in the unit, we will work with non-right
triangles.
Labeling Triangles for Trig
hypotenuse
opposite
adjacent
You try…
Sine of ∠Ө
Opposite
=
Hypotenuse
Ө
Cosine of ∠ Ө
Adjacent
=
Hypotenuse
Ө
Tangent of ∠ Ө
Opposite
=
Adjacent
Ө
soh cah toa
soh cah toa
Write the 3 Trig Functions for each angle. (A and C)
We never use the 90o angle!
sin A =
sin C =
cos A =
cos C =
tan A =
tan C =
Example 2: Finding a Side Length
Use a Trig Function and solve using Algebra!
Find x.
When you need to use your calculator, ALWAYS
make sure it’s in DEGREE mode
Example 3: Finding a Side Length
Use trig to solve for x.
Example 4: Working backwards
Find the measure of angle C.
Now our three trig functions can be
used to find the measure of an angle!
sin
sin-1(
)
cos
cos-1(
)
tan
tan-1(
)
Example 6: Find Angle M.
Am I finding an angle or a side?
Angle
Side
Sine, cosine or
tangent?
Sine, cosine, or tangent?
Use the inverse
function.
Use algebra to solve for
the missing side.
Example 1: Hot Air Balloon
As a hot-air balloon began to rise, the ground crew
drove 1.2 mi to an observation station. The initial
observation from the station estimated the angle
between the ground and the line of sight to the
balloon to be 30º. Approximately how high was the
balloon at that point? ‘
The balloon is approximately 0.7 mi, or 3696 ft, high.
Example 2: Width of a River
A surveyor can measure the width of a river by standing
on point C and taking a sighting at point A on the other
side. After turning 90° and walking 200m, he takes
another sighting from point B. Angle B is measured and
found to be 20°. What is the width of the river?
The width of the river is approximately 73 meters.
Example 3: Painting a House
For safety reasons, the base of a
25 ft must be 6.5 ft from the
base of wall. At what angle
with the ground should a
painter place his ladder in
order to maximize his height?
Thus when the ladder is in its safest position, it makes
an angle of about 75º with the ground.