7.3 day 2 the law of cosines -...
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7.3 Day 2 The Law of Cosines
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May 05, 2009
Apr 19 9:19 AM
Objective: Use the law of cosines to find measures of sides and
angles in triangles.
7.3 The Law of Cosines
Day 2
7.3 Day 2 The Law of Cosines
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May 05, 2009
Apr 20 3:03 PM
Law of Cosines: For any triangle with sides a, b, c and opposite angles α, β, γ, respectively, the following is true.
a
α
γβ
bc
c2 = b2 + a2 2ab cos γ
b2 = a2 + c2 2ac cos β
a2 = b2 + c2 2bc cos α
((β = cos1 a2 + c2 b2
2ac
((α = cos1 b2 + c2 a2
2bc
(( a2 + b2 c2
2abγ = cos1
7.3 Day 2 The Law of Cosines
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May 05, 2009
Apr 20 3:29 PM
Example #1: The distance from home plate to the fence in dead center at the Oak Lawn Little League field is 280 feet. How far is it from the fence in dead center to third base?Hint: The distance between the bases in Little League is 60 feet.
280
60
?
241.33 feet
7.3 Day 2 The Law of Cosines
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May 05, 2009
Apr 20 3:29 PM
Example #2: A cruise ship maintains an average speed of 15 knots in going from San Juan, Puerto Rico, to Barbados, West Indies, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan in a direction of 20o off the direct heading to Barbados. The captain maintains the 15knot speed for 10 hours, after which time the path to Barbados becomes clear of storms.
600
20o
Barbados
San Juan
7.3 Day 2 The Law of Cosines
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May 05, 2009
Apr 20 3:29 PM
Example #2: A cruise ship maintains an average speed of 15 knots in going from San Juan, Puerto Rico, to Barbados, West Indies, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan in a direction of 20o off the direct heading to Barbados. The captain maintains the 15 knot speed for 10 hours, after which time the path to Barbados becomes clear of storms.
a. Through what angle should the captain turn to head directly to Barbados?
Step 1: Find the distance traveled.15(10) = 150 nautical miles
Step 2: Find the distance remaining.d2 = 6002 + 1502 2(600)(150)cos20od = 461.9 nautical miles
Step 3: Find the angle towards Barbados.
Step 4: Find the angle the captain should turn.
600
20o
Barbados
San Juan
sinS600
sin20o461.9=
sinS 600sin20o 461.9=
sinS = 0.444278
S = sin1(0.444278)S = 26.4o or 180o 26.4o = 153.6o
180o 153.6o = 26.4o
7.3 Day 2 The Law of Cosines
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May 05, 2009
Apr 20 3:29 PM
Example #2: A cruise ship maintains an average speed of 15 knots in going from San Juan, Puerto Rico, to Barbados, West Indies, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan in a direction of 20o off the direct heading to Barbados. The captain maintains the 15 knot speed for 10 hours, after which time the path to Barbados becomes clear of storms.
b. Once the turn is made how long will it be before the ship reaches Barbados if the same 15 knot speed is maintained?
Yay...we already found the distanceto be 461.9 nautical miles. Now we haveto convert that into time at 15 knot/hour.
461.9 ÷ 15 = 30.8 hours
600
20o
Barbados
San Juan
7.3 Day 2 The Law of Cosines
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May 05, 2009
Apr 20 3:56 PM
HOMEWORKpage 547 (33, 36, 38, 39, 41, 48)