Transcript solve right triangles

Chapter 9
Right Triangles and Trigonometry
Section 9.6
Solving Right Triangles
SOLVE RIGHT TRIANGLES
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
9.6
Solving Right Triangles
SOLVE RIGHT TRIANGLES
CONCEPT
Solving Right Triangles
SUMMARY
To Solve A Right Triangle: Determine the measure of all three
angles and the length of all three sides.
C
1. Three Angles
•
a
ab
A, B, C
2. Three Sides
c
9.6
B
Solving Right Triangles
•
a, b, c
SOLVE RIGHT TRIANGLES
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
Example 1
Given 1 Side and 1 Angle
Example 2
Given 2 Sides
Example 3
Solving Real Life Problems
Homework
9.6
Solving Right Triangles
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 1 Side, 1 Angle
10.4
19
30.3
X & Y are Complements
mX + mY =90
71 + mY =90
mY = 19
9.6
Solving Right Triangles
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 1 Side, 1 Angle
Find AB, AC, mA
AB
tan 52 
19
19 tan 52  AB
AB  24.319
cos 52 
19
AC
AC (cos 52)  19
19
AC 
cos 52
AC  30.861
9.6
Solving Right Triangles
mA + mC = 90
mA + 52 = 90
mA = 38
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 1 Side, 1 Angle
mN = 55
9.6
MN
sin 35 
9
MN  5.162
LM
cos35 
9
LM  7.372
Solving Right Triangles
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
9.6
Solving Right Triangles
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
=12
mA + mB = 90
mA + 33.69 =90
mA  67.38
5
B  tan
 22.62
12
1
9.6
Solving Right Triangles
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
Use the Pythagorean theorem to find XZ
(XZ)2 + 142 = 252
(XZ)2 + 196 = 225
(XZ)2 = 29
XZ  29
9.6
Solving Right Triangles
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
Need to find X
14
sin X 
25
1 14
sin
X
25
mX  34.06
9.6
Solving Right Triangles
mX + mY = 90
34.06 + mY = 90
mY  55.94
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
ML  340  2 85  18.439
mM  tan 1
12
 40.601
14
mL  49.399
9.6
Solving Right Triangles
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
CIRCUS ACTS At the circus, a person in the audience
watches the high-wire routine. A 5-foot-6-inch tall
acrobat is standing on a platform that is 25 feet off the
ground. How far is the audience member from the
base of the platform, if the angle of elevation from the
audience member’s line of sight to the top of the
acrobat is
Make a drawing.
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
Since QR is 25 feet and RS is 5 feet 6 inches or 5.5 feet,
QS is 30.5 feet. Let x represent PQ.
Multiply both sides by x.
Divide both sides by tan
Simplify.
Answer: The audience member is about 60 feet
from the base of the platform.
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
SHORT-RESPONSE TEST ITEM
A wheelchair ramp is 3 meters long and inclines at
Find the height of the ramp to the nearest tenth
centimeter.
Solve the Test Item
Method 1
The ground and the horizontal level with the platform
to which the ramp extends are parallel. Therefore,
since they are alternate interior
angles.
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
Y
W
Mulitply each side by 3.
Simplify.
Answer: The height of the ramp is about 0.314 meters,
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
SHORT-RESPONSE TEST ITEM
A roller coaster car is at one of its highest points. It
drops at a
angle for 320 feet. How high was the
roller coaster car to the nearest foot before it began
its fall?
Answer: The roller coaster car was about 285 feet above
the ground.