Law of Sin Cos Stories Solutions.notebook
December 08, 2015
1. To measure the height of a mountain, a surveyor takes two sightings of the
peak at a distance 900 meters apart on a direct line to the mountain. The first
observation results in an angle of elevation of 47°, and the second results in
an angle of elevation of 35°. If the transit is 2 meters high, what is the height
h of the mountain?
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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
2. A motorized sailboat leaves Naples, Florida, bound for Key West, 150 miles
away. Maintaining a constant speed of 15 miles per hour, but encountering
heavy crosswinds and strong currents, the crew finds, after 4 hours, that the
sailboat is off course by 20°.
How far is the sailboat from Key West?
Through what angle should the sailboat turn to correct the course?
How much time has been added to the trip because of this? (Assume that the
speed remains at 15 miles per hour.)
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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
3. The distance from the Sun to Earth is approximately (on average)
149,600,000 kilometers. The distance from the Sun to Mercury is
approximately (on average) 57,910,000 km. The elongation angle α is the angle
formed between the line of sight from Earth to the Sun and the line of sight
from Earth to Mercury. See the figure. Suppose the elongation angle for
Mercury is 15°. Use this information to find the possible distances between
Earth and Mercury.
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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
4. Coast Guard Station Zulu is located 120 miles due west of Station X-ray. A
ship at sea sends an SOS call that is received by each station. The call to
Station Zulu indicates that the bearing of the ship from Zulu is N40°E (40°
east of north). The call to Station X-ray indicates that the bearing of the ship
from X-ray is N30°W (30° west of north).
How far is each station from the ship?
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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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
5. A Major League baseball diamond is actually a square 90 feet on a side. The
pitching rubber is located 60.5 feet from home plate on a line joining home
plate and second base.
How far is it from the pitching rubber to first base?
How far is it from the pitching rubber to second base?
If a pitcher faces home plate, through what angle does he need to turn to face
first base?
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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
6. The distance from home plate to the fence in dead center in Wrigley Field is
400 feet (see the figure). How far is it from the fence in dead center to third
base?
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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
7. To find the length of the span of a proposed ski lift from P to Q, a surveyor
measures DPQ to be 25° and then walks off a distance of 1000 feet to R and
measures PRQ to be 15°. What is the distance from P to Q?
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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
8. A golfer hits an errant tee shot that lands in the rough. A marker in the
center of the fairway is 150 yards from the center of the green. While standing
on the marker and facing the green, the golfer turns 110° toward his ball. He
then paces off 35 yards to his ball. See the figure. How far is the ball from the
center of the green?
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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
9. An awning that covers a sliding glass door that is 88 inches tall forms an
angle of 50° with the wall. The purpose of the awning is to prevent sunlight
from entering the hours when the angle of elevation of the sun is more than
65°. See the figure. Find the length L of the awning.
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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
10. 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 60°. Find RPQ indicated in the figure. Also,
find the perpendicular distance from R to PQ.
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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
11. A loading ramp 10 feet long that makes an angle of 18° with the
horizontal is to be replaced by one that makes an angle of 12° with the
horizontal. How long is the new ramp?
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Law of Sin Cos Stories Solutions.notebook
December 08, 2015
12. A radio tower 500 feet high is located on the side of a hill with an
inclination to the horizontal of 5°. See the figure. How long should two guy
wires be if they are to connect to the top of the tower and be secured at two
points 100 feet directly above and directly below the base of the tower?
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