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7.1 Day 2 Right Triangle Trigonometry; Applications
1
April 28, 2009
Apr 257:05 PM
7.1 Right Triangle Trigonometry; ApplicationsDay 2
Objective: Solve right triangle trigonometry application problems.
7.1 Day 2 Right Triangle Trigonometry; Applications
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Apr 257:05 PM
Example #1: A right triangle contains an angle of radian. If one leg is 5 meters long, what is the length of the hypotenuse?
π7
Hint: Remember to change calculator to radians!!!
5 xπ7
π7
5
x
cos = π7
5x
x = 5cos π7
x ≈ 5.55 meters
sin = π7
5x
x = 5sin π7
x ≈ 11.52 meters
7.1 Day 2 Right Triangle Trigonometry; Applications
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Line of
sight
Angle of elevation
Object
Vertical heights can sometimes be measured using either the angle of elevation or the angle of depression.
Horizontal
Line of sight
Angle of depression
Object
7.1 Day 2 Right Triangle Trigonometry; Applications
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25o100 ft
Example #2: A ship, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the cliff. If the angle of elevation is found to be 25o, how far offshore is the ship?
tan 25o = 100 xx =
x ≈ 214.45 feet
100tan 25o
x
7.1 Day 2 Right Triangle Trigonometry; Applications
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In navigation and surveying, the direction or bearing from a point O to a point P equals the acute angle θ between the ray OP and the vertical line through O, the northsouth line.
30o
70o
50o
20o
P1P3
P2P4
N
EW O
N30OE
N70OW
S50OWS20OES
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Example #3: A Boeing 777 aircraft takes off from O'Hare Airport on runway 2 LEFT, which has a bearing of N20oE. After flying for 1 mile, the pilot of the aircraft requests permission to turn 90o and head toward the northwest. The request is granted. After the plane goes 2 miles in this direction, what bearing should the control tower use to locate the aircraft?
tan θ = 21θ = tan1(2)
θ ≈ 63.4o
20o
N
E
S
WRunway 2 LEFT
θ 1
2
P
Q
O
63.4o 20o = 43.4o
The bearing of the aircraft from O to Q is N43.4oW.
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Homework: page 528 (43, 46, 54, 57, 64, 67, 70)
