8.1d – LAW OF SINES (Day 4)
LESSON NOTES
MA42-S9C5-01,05
OBJECTIVE: TSWD analysis of “Real World” Trig problems by examining a problem, identifying
& Classifying the important information, and then solving the problem using the Law of Sines.
REAL WORLD APPLICATION
1.
AREA OF A TRIANGULAR LOT: Find the area of a triangular lot having two sides of lengths
20 yards and 30 yards and an included angle of 60º.
2.
TILTING POLE: A pole tilts toward the sun at an 8º angle from the vertical, and it casts a 22-foot
shadow. The angle of elevation from the tip of the shadow to the top of the pole is 43º. How tall is the
pole?
3.
TRIANGULATE POSITION: Coast Guard Station Able is 150 miles due south of Station Baker. A
ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that
the ship is located N55ºE; the call to Station Baker indicates that the ship is located S60ºE.
(a) How far is each station from the ship?
(b) If a helicopter capable of flying 200 miles per hour is
dispatched from the nearest station to the ship, how
long will it take to reach the ship?
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4.
TILTING POLE w/PERPENDICULAR DISTANCE: The famous Leaning Tower of Pisa was originally
184.5 feet high. At a distance of 123 feet from the base of the tower, the angle of elevation to the top
of the tower is found to be 60º. Find the angle CAB indicated in the figure. Also, find the
perpendicular distance from C to AB.
SUMMARIZE CONCEPTS & TERMS
I.
“Angle from the horizontal”
“Angle of depression”
II.
“Angle from the vertical”
“Angle of elevation”
“Perpendicular distance”
“Turns thru an Angle”
Bearings
There are two ways to express a navigational heading or “bearing.”
1. When a single angle is given, it is understood that the bearing is
measured in a clockwise direction from due north.
Example: The bearing from A to C is 30º.
2. The other system starts with a north or south line and uses an
acute angle to show direction.
Example: The bearing from A to C is S 52º E (52º East of South)
a. bearing of 320
b. bearing of 3040
c. N 420 E
d. S 310 E
e. N 520 W
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