Download Pre Cal 4.3 PPT and assign

4-3 Right Triangles
Objectives:
•Solve right triangles
•Solve measurement
problems using
trigonometry
©2002 Roy L. Gover (www.mrgover.com)
Important Idea
For any two
triangles with
y
congruent
angles,
regardless of
size, the ratio
y’
of
corresponding
sides are equal.
r
x
r’
x’
Find the
Example
values of
the 6 trig
functions of 8 cm.
17 cm.

. Leave

your
answers as
15 cm.
a fraction.
Find the
Try This
values of
the 6 trig
functions of 13 cm.
12
cm.
. Leave


your
answers as
5 cm.
a fraction.
Solution
12
sin  
13
5
cos  
13
12
tan  
5
13
csc  
12
13
sec  
5
5
cot  
12
Solve triangle
Example
ABC. Round
angle
C 12
B
measures to
the nearest
b
c
degree & side
52°15’
measures to
the nearest
A
tenth.
Example
Step 1: Draw
& label
C 12
B
Step 2: Solve
b
for the
c
missing angle
52°15’
Step 3: Write
A
trig equations
& solve for the missing sides
Solve triangle
ABC. Round
angle
measures to
the nearest
degree & side
measures to
the nearest
tenth.
Try This
49°12’
b
A
c
C
7
B
Solution
C=90°
B =40.8°
c  9.2
b  6.0
49°12’
b
A
c
C
7
B
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.
Example
Find the angle whose

sin is
.
4
Stated another way:
Find

 when sin   4
Try This
Find the angle whose tan is
1.2382. State your answer in
degrees and radians to the
nearest tenth.
51.1° or .9 rads
Try This
R
S
In triangle
TRS, find
10
12
the measure
of angle T in
degrees and
T
rads to the
nearest
33.6° or .6 rads
tenth..
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.
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?
Example
2. If she starts descending
170.5 miles (900,000 feet)
from the airport, what
angle will the plane make
with the horizontal?
Example
What is the
tallest
building a
ladder truck can reach if the

angle of the ladder is 3 radians,
the length of the ladder is 108 ft.
and the ladder is mounted on
the truck 8 ft. from the ground.
Thanks to James Anania 4th 1.21.09
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?
Solution
1. Draw & label:
2. Write an
equation & solve 20°
64.1 ft.
x
176 ft
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.
Assignment
Practice pages 310-313
#1, 5, 9, 13, 17, 21, 33,
37, 41, 45, 57, 61, 65, 67,
71