Chapter 5 Introduction to
Trigonometry
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
Goals for Today:
• Apply what we learned yesterday about right
triangles and trigonometry to solve word
problems
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
Ex. 1 We have a video camera at the top of a
shorter office building. It can tilt up 47° to see
the top of an adjacent taller building. It can tilt
down 36° to see the bottom of the adjacent
building.
(a) How far apart are the buildings?
(b) How tall is the large building?
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
Ex. 1
47°
120m
36°
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
Ex. 1 (a) How far apart are the buildings?
• The height of the
bottom triangle is also
120m, so we have a side
opposite the 36° angle.
To find how far apart the
buildings are, we need to
find the side adjacent to
36°, using the TAN ratio
47°
120
m
3
6
°
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
Opposite
TanA 
Adjacent
120
Tan36 
x
120
0.7265 
x
120
)( x)
( x)(0.7265)  (
x
120
0.7265
x
0.7265
0.7265
x=165.2m
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
Ex. 1 (b) How tall is the large building?
•We know that the
bottom of the top
triangle is 165.2m. We
can use that length and
the 47° angle. To find
how tall the larger
building is, we need to
find the side opposite the
47°, using the TAN ratio
and then add it to 120m
47°
120
m
3
6
°
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
Opposite
TanA 
Adjacent
x
Tan47 
165.2
x
1.0724 
165.2
x
)(165.2)
(165.2)(1.0724)  (
165.2
x  177.2
Therefore, the total height is 120m  177.2m  297.2m
Humour Break
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
Ex. 2 An 12.5m high antenna is held by guy wires
that are 16m long. These wires are anchored
to the roof of a building.
(a) What is the angle of the guy wires with the
roof?
(b) What is the distance of each anchor from the
antenna?
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
16m
16m
12.5m
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
(a) What is the angle of
the guy wires with the
roof? From the anchor
angle on the roof, we
are dealing with the
opposite side (the
height of the antenna)
and the hypotenuse
(the guy wire). So, we
use the SIN ratio
1
6
m
1
6
m
1
2
.
5
m
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
(a) What is the angle of the guy wires with the
roof?
Opposite
Sin A 
Hypotenuse
12.5
Sin A 
16
Sin A  0.7813
A  51.4
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
(a) What is distance from
the base of the
antenna to the anchor.
From the anchor angle
we now know, we can
use the COS ratio
working with the
known hypotenuse and
the unknown adjacent
side
1
6
m
1
6
m
1
2
.
5
m
5.8 Solving Problems Using Right
Triangle Models and Trigonometry
(b) What is distance from the base of the
antenna to the anchor?
Adjacent
CosA 
Hypotenuse
x
Cos51.4 
16
x
0.6239 
16
x
(16)( 0.6239)  ( )(16)
16
x  10m
Homework
• P.509, #1-15 & 17 & 18