
James B. answered 07/21/16
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(1)
C |
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| 65º
B |______________________ A
24 ft
The height of the pole is side BC.
Angle A is 65º
tangent A = opposite/adjacent
tangent 65º = AB/24
AB/24 = tangent 65º
AB = (24)•tangent 65º
AB = 24(2.14451)
AB = 51.47 ft
Flagpole is approximately 51.47 ft tall.
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(2)
C |
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| 18 ft
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B |_________ A
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| 18 ft
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B |_________ A
We need to determine angle A.
Side AC es the ladder, which is 20 ft.
We need the ladder to be 18 feet up the side of the building (side BC)
sine A = opposite/hypotenuse
= 18/20
= 9/10
=.9
A = sine-1(.9)
A = 64.16º
Angle A is approximately 64.16 degrees.
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(3)
A ___________ B
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\ 80º /
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\/
C
We are looking for side BC.
Since rate x time is distance, we can find the length of AB. Rate is 20 mph and time is 2 hours
(20)(2) = 40 ... side AB is 40
Similarly, we can find the length of AC. Rate is 14 mph and time is 2 hours.
(14)(2) = 28 ... side AC is 28
We can use the law of cosines to find side BC.
a2 = b2 + c2 - 2bc• cos A
= (28)2 + (40)2 - 2(28)(40)•cos 80º
= 784 + 1600 - 2240(.17365)
= 2384 - 388.97
= 1995.03
a = √(1995.03)
= 44.67
Thus, the 2 boats are 44.67 miles apart.