Transcript 8.7 Applications of Trigonometry

Geometry
8.7 Applications of
Right Triangle Trigonometry
Vocab
• Add hypotenuse, the three proportions,
Pythagorean Theorem and Converse,
multiply fractions vs. proportions, 45-45-90
and 30-60-90 formulas, pythagorean
triples, sine, cosine, tangent, angle of
elevation, angle of depression to vocab list
Solving Word Problems
Use the 3 ratios – sin, cos and tan to
solve application problems.
Choose the easiest ratio(s) to use
based on what information you are
given in the problem.
Depression and Elevation
If a person on the ground
looks up to the top of a
building, the angle
formed between the line
of sight and the
horizontal is called the
angle of elevation.
angle of depression
angle of elevation
If a person standing on
the top of a building
looks down at a car on
the ground, the angle
formed between the
line of sight and the
horizontal is called the
angle of depression.
horizontal
horizontal
1.
From a point 80m from the base of a tower, the angle of elevation to the top of the tower is 28o.
How tall is the tower?
1. From a point 80m from the base of a tower, the
angle of elevation is 28˚. How tall is the tower?
x
28˚
80
Using the 28˚ angle as a reference, we know opposite and adjacent sides.
opp
Use
adj
tan
tan 28˚ =
x
80
80 (tan 28˚) = x
80 (.5317) = x
x ≈ 42.5
About 43 m
2.
A ladder that is 20ft. is leaning against the side of a building. If the angle formed between the ladder
and the ground is 75o, how far is the bottom of the ladder from the base of the building?
2. A ladder that is 20 ft is leaning against the side
of a building. If the angle formed between the ladder
and ground is 75˚, how far is the bottom of the
ladder from the base of the building?
building
20
75˚
x
Using the 75˚ angle as a reference, we know hypotenuse and adjacent side.
adj
x
Use
cos 75˚ =
cos
hyp
20
20 (cos 75˚) = x
20 (.2588) = x
x ≈ 5.2
About 5 ft.
3.
When the sun is 62o above the horizon, a building casts a shadow 18m long. How tall is the building?
3. When the sun is 62˚ above the horizon, a
building casts a shadow 18m long. How tall is
the building?
x
18
62˚
shadow
Using the 62˚ angle as a reference, we know opposite and adjacent side.
opp
x
Use
tan 62˚ =
tan
adj
18
18 (tan 62˚) = x
18 (1.8807) = x x ≈ 33.9
About 34 m
4. A kite is flying at an angle of elevation of about 55o. Ignoring the sag in the string, find the height of
the kite if 85m of string has been let out.
4. A kite is flying at an angle of elevation of about
55˚. Ignoring the sag in the string, find the height of
the kite if 85m of string have been let out.
kite
85
x
55˚
Using the 55˚ angle as a reference, we know hypotenuse and opposite side.
opp
x
Use
sin 55˚ =
sin
hyp
85
85 (sin 55˚) = x
85 (.8192) = x
x ≈ 69.6
About 70 m
6.
The angle of depression from the top of a tower to a boulder on the ground is 38o. If the tower is 25m high,
how far from the base of tower is the boulder?
6. The angle of depression from the top of a tower to a
boulder on the ground is 38º. If the tower is 25m high,
how far from the base of the tower is the boulder?
38º
angle of depression
Alternate Interior Angles are congruent
25
38º
x
Using the 38˚ angle as a reference, we know opposite and adjacent side.
opp
Use
tan
tan 38˚ = 25/x
adj
(.7813) = 25/x
X = 25/.7813
x ≈ 32.0
About 32 m
Homework
• Finish Notes problems #5 and #7
on binder paper.
Answers: #5: 83m
#7: 27m
Do pg. 318 #1-6
•Vocab Test Tomorrow, Test Thursday
•