1. 6-2: Trignometric
Applications
© 2007 Roy L. Gover (www.mrgover.com)
Learning Goals:
•Solve applications using
triangles
•Solve triangles using
trigonmetric ratios

2. Important Idea
Triangle Sum Theorem: The
sum of the measures of the
angles in a triangle is 180°.
Pythagorean Theorem: In a
right triangle with legs a and
b and hypotenuse c, a2
+b2
=c2

3. Important Idea
For any two
triangles with
congruent
angles,
regardless of
size, the ratio of
corresponding
sides are equal.
y
y’
r
r’
x
x’

4. Example
α
17 cm.8 cm.
15 cm.
Find the
values of
the 6 trig
functions of
. Leave
your
answers as
a fraction.
α

5. Try This
β
13 cm.
5 cm.
12 cm.
Find the
values of
the 6 trig
functions of
. Leave
your
answers as
a fraction.
β

6. Solution
12
sin
13
5
cos
13
12
tan
5
β
β
β
=
=
=
13
csc
12
13
sec
5
5
cot
12
β
β
β
=
=
=

7. Example
A
BC 12
52°15’
b c
Solve triangle
ABC. Round
angle & side
measures to
the nearest
tenth.

8. Example
A
BC 12
52°15’
b c
Step 1: Draw
& label
Step 2: Solve
for the
missing angle
Step 3: Write
trig equations
& solve for the missing sides

9. Try This
A
B
C
7
49°12’
b
c
Solve triangle
ABC. Round
angle and
side
measures to
the nearest
tenth.

10. Solution
A
B
C
7
49°12’
b
c
C=90°
B =40.8°
c ≈ 9.2
b ≈ 6.0

11. Definition
Inverse Trig Function: the
function that gives the angle
whose trig value is known.
Inverse trig functions are
known as an arc or inverse
function.

12. Example
Find an angle whose
sin is .
θ
Stated another way:
Find when
2
sin
2
θ =
2
2

13. Definition
The inverse trig functions
are:
1
1
1
sin
cos
tan
x
x
x
θ
θ
θ
−
−
−
=
=
=
arcsin
arccos
arctan
x
x
x
θ
θ
θ
=
=
=
or

14. Example
Stated another way:
Find the angle whose cos
is .523.
Find (arccos .
523)
1
cos .523−

15. Try This
Find . State your
answer in degrees to the
nearest tenth.
51.1°
1
tan 1.2382−

16. Example
T
R S
12
In triangle
TRS, find
the measure
of angle T in
degrees to
the nearest
tenth..
5

17. Try This
T
R S
12
10
In triangle
TRS, find the
measure of
angle T in
degrees to the
nearest tenth.
Don’t forget to
check “mode”. 33.6°

18. ExampleA 16 foot ladder is
placed against
the side of a
house. The base
of the ladder
makes a 60°
angle with the
ground. How far
up the side of the
house will the
ladder reach?

19. ExampleA ladder reaches
17 feet up the
side of a house.
If the base of the
ladder makes an
angle of 62° with
the ground, how
long must the
ladder be?

20. ExampleA 25 foot ladder
reaches 20 feet
up the side of a
house. What is
the angle the
ladder makes with
the ground?

21. Example
Commercial
airliners fly at an altitude of
30,000 feet. They start
descending toward the
airport when they are far
away so they will not have to
dive at a steep angle to land.

22. Example
1. If the pilot wants the plane
to descend at an angle of 3°,
at what horizontal distance
from the airport must she
start her descent?

23. Example
2. If she starts descending
170.5 miles (900,000 feet)
from the airport, what angle
will the plane make with
the horizontal?

24. ExampleWhat is
the tallest
building a
ladder
truck can reach if the angle
of the ladder is 60°, the
length of the ladder is 108 ft.
and the ladder is mounted on
the truck 8 ft. from the
ground.

25. Try This
The sun casts a
shadow 176 ft. long
when it shines over a
flagpole with an angle of
elevation of 20°. What is
the height of the flagpole?

26. Solution
1. Draw & label:
20°
176 ft
x
2. Write an
equation & solve
64.1 ft.

27. Try This
A girl spots a
tree with an
angle of
elevation of 25°
the tree and an angle of
depression of 15° to the
bottom of the tree from eye
level. Her eye level is 165 cm.
How far is the girl from the
tree? How high is the tree?
to the top of

28. Try This
25°
15°
165cm
Distance to tree: 615.8 cm
Height of tree: 452.2 cm

29. Lesson Close
On a sheet of paper, make
up a right triangle problem
and solve it. Draw & label
a sketch, show all your
work and circle your
answer.