2.5 - more right triangle word problems -...
TRANSCRIPT
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2.5 - More Right Triangle Word Problems
In Navigation, they give angles in BEARINGS.
A plane flies 200 miles with a Bearing of 70o
Bearing: TYPE 1
BEARING ( aka heading or course ):***The angle is measured from the North going clockwise
N
EW
70 o200 mi
S
2
Bearing 120 o Bearing 300 o
Bearing 24 oBearing 215 o
Bearing 95 oBearing 190o
N
S
EW
N
S
EW
N
S
EW
N
S
EW
N
S
EW
N
S
EW
Bearing: TYPE 2 ***The angle is sandwiched between to directions
A boat is traveling 50 mph for 3 hrs on a bearing of S 20o E.
150 miles
N
S
EW
20 o
150 mi
From the South turn 20o to the East
3
N 25o W N 50o E
S 80o W S 60o E
Always starts N or S then turns an ACUTE ANGLE E or W
N
W
S
E
N
W
S
E
N
W
S
E
N
W
S
E
It is critical that your drawing is neat, accurate, and labeled!!!
1.) Read the problem.2.) Sketch a diagram.3.) Find and label the RIGHT TRIANGLE.4.) Set up an Equation and solve.5.) Answer the question.
Steps for Story Problems
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The bearing from Atlanta to Macon is S 27o E, and the bearingfrom Macon to Augusta is N 63o E. A car traveling 60 mph
needs 1 1/4 hrs to go from Atlanta to Macon and 1 3/4 hrs to go from Macon to Augusta. Find the distance and
bearing from Atlanta to Augusta.
27o
75
A
63o 105
M
? AugA
M
27o
d = rtd = 60(1.25)d = 75 mi
d = rtd = 60(1.75)d = 105 mi
c 2 = 752 + 1052
c≈129 milesTan A = 105 75
A≈54.5
o
oAnswer : 129 miles with a bearing of S 81.5 o E
54.5 o
5
The angle of elevation to the top of a building is 41o. When you walk 168 ft closer to the building, the angle of elevation is 530. How tall is the building?
41 o
168 + x
h
x53 o
htan 53 = h x
x tan 53 =htan 41 = h x + 168
tan 41 ( x + 168 ) = h
x tan 41 + 168 tan 41 = h
x tan 53 = x tan 41 + 168 tan 41
x tan 53 = x tan 41 + 168 tan 41
x tan 53 - x tan 41 = 168 tan 41
x ( tan 53 - tan 41 ) = 168 tan 41
x = 168 tan 41 ( tan 53 - tan 41 )
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tan 53 = h xx tan 53 = h
But they asked for the height!
tan 53 =h 168 tan 41 ( tan 53 - tan 41 )
pg. 81: 11, 12, 13, 15, 23, 25