Transcript UNIT 33

Unit 35
PRACTICAL APPLICATIONS
WITH RIGHT TRIANGLES
PROBLEMS STATED IN WORD FORM

Procedure for solving right triangle
problems stated in word form:
1. Sketch a right triangle based on the given
information
2. Label the known parts of the triangle with the
given values. Label the angle or side to be found
3. Follow the procedure for determining an unknown
angle or side of a right triangle
2
ANGLES OF DEPRESSION AND
ELEVATION

Two terms commonly used in practical application
problems from various occupational fields are the
angle of depression and the angle of elevation. The
illustration below shows what is meant by these two
terms
Horizontal Line
Horizontal Line
Angle of
elevation
Line of sight
3
EXAMPLE

A surveyor is to determine the height of a
TV relay tower. The transit is positioned at
a horizontal distance 20 meters from the
foot of the tower. An angle of elevation of
46° is read in sighting the top of the tower.
The height from the ground to the transit
telescope is 1.70 meters. Determine the
height of the tower to the nearest
hundredth of a meter.

Sketch a picture and label the parts
4
EXAMPLE (Cont)
–
Sketch a picture and label the parts
Line of
sight
Transit
–
–
46°
20 m
Tower
(T)
Solve: tan 46° = (T/20) so T = 20.71 m
Now add the height of the transit:
20.71 m + 1.70 m = 22.41 meters An
5
EXAMPLE
Some problems require forming two or
more right triangles by projecting auxiliary
lines. Compute linear values to two
decimal places.
 Compute the length of piece AB of the roof
A
B
truss.

2.20m
35.3°
28.5°
10.30m
6
EXAMPLE (Cont)
Compute the length of piece AB of the
roof truss.
 Drop two vertical lines to create right
triangles.

A
B
2.20m
28.5°
35.3°
10.30m
7
EXAMPLE (Cont)
• Compute the length of piece AB of the roof truss.
A
2.20m
B
28.5°
35.3°
10.30m
2.2

tan 35.3 
adjacent
2.2
0.7080 
adjacent
adjacent  3.1m
tan 28.5 
2.2
adjacent
0.54296 
2.2
adjacent
adjacent  4.05m
10.30m  3.1m  4.05m  3.14m Ans
8
A right circular conical tank has a height of 4 m and a
radius of 1.2 m. The tank is filled to a height of 3.7 m with
liquid. How many liters of liquid are in the tank?

Think in a 2
dimensional sense
 See
the right triangle
created by the top
side, and altitude
 See the one created
by the top of the water,
side, and altitude
9
A right circular conical tank has a height of 4 m and a radius of 1.2 m. The tank is filled to
a height of 3.7 m with liquid. How many liters of liquid are in the tank?



We can work with
trigonometry or
similar triangles to
solve this one
Since we are working
with trig we will go
that direction although
they are similar.
In both triangles, the
angle at the bottom of
the vessel is the
same.
10
A right circular conical tank has a height of 4 m and a radius of 1.2 m. The tank is filled to
a height of 3.7 m with liquid. How many liters of liquid are in the tank?

So by figuring out the
red right triangle’s
bottom angle we have
the purple one as well
1.20
sin  
4.00
  17.46
11
A right circular conical tank has a height of 4 m and a radius of 1.2 m. The tank is filled to
a height of 3.7 m with liquid. How many liters of liquid are in the tank?

Now that we know the
angle is 17.46 we can
redo our last slides
opp
work
sin 17.46 
3.70
opp  1.11m

That tells us that the
water has a radius of
1.11m the .3m below
12
A right circular conical tank has a height of 4 m and a radius of 1.2 m. The tank is filled to
a height of 3.7 m with liquid. How many liters of liquid are in the tank?

So we know the water is 3.7 m deep and has a
radius of 1.11m at the top. The vessel is in a
shape of a right cone
2
3
1
V   (1.11) ( 3.7 )  4.77m
3

That does not finish the question though
3
4.77m
1000L
x
 4770Liters
3
1
1m
13
PRACTICE PROBLEMS
1.
2.
Measuring out a horizontal distance of 65 feet on the
ground from the base of a tower and then sighting the
top of the tower from that position results in an angle of
elevation of 54°. Determine the height of the tower to
the nearest hundredth of a foot.
A highway entrance ramp rises 38.4 feet in a horizontal
distance of 154.8 feet. Determine the angle of
inclination of the ramp.
14
PRACTICE PROBLEMS (Cont)
3.
4.
A conveyor belt is used by Patty’s
Packaging Company to lift packages. The
most efficient operating angle is 33.25°. If
the packages are elevated 4.75 feet, how
long is the conveyor belt?
A flower bed shaped like a right triangle
has sides of 5.4 feet, 3.2 feet, and 4.35
feet. What are the measures of the two
acute angles formed by the bed in DMS?
15
PRACTICE PROBLEMS (Cont)
5.
Determine the gauge dimension y of the V-block below. EF and GF are
equivalent. Round to 3 decimal places.
16
PROBLEM ANSWER KEY
1.
2.
3.
4.
5.
89.46 feet
13.9°
8.66 feet
36° 18’ and 53° 42’
0.37 in
17