How Lighthouses Are Built
how lighthouses are built
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Ugh.... Law of Sines Word Problems? Help ME.?
So I don't really have a graphing calculator....
1. In triangle ABC, angle A= 65, B=70, and the side opposite vertex B is 7. Find the length of the side opposite vertex A, and find the area of triangle ABC.
I did:
7/sin70 = A/sin 65
7(sin65)/sin 70 = side a = 6.75
and for the area:
1/2(7)(6.75)(sin45)= 16.71.
2. While sailing on a boat offshore, Donna sees a lighthouse and calculates that the angle of elevation to the top of the lighthouse is three degrees. When she sails her boat 700 feet closer to the lighthouse, she finds that the angle of elevation is now 5 degrees. How tall, to the nearest tenth of a foot, is the lighthouse?
3. A sign 46 feet high is placed on top of an office building. From a point on the sidewalk level with the base of the building, the angle of elevation to the top of the sign and the angle of elevation to the bottom of the sign are 40 degrees and 32 degrees respectively. Find the height of the building to the nearest foot.
Problem 1. Your answers are correct. Good work!
Problem 2. A sketch is always useful. If you draw a
vertical line to represent the lighthouse and from the
base of this vertical line, a horizontal line to represent the ocean, then you have a 90 degree angle/.
The 2 observation points give you 2 right triangles.
What these 2 triangles have in common is the height
h of the lighthouse. We shall use this common side
to solve the problem.
Let x be the distance from the lighthouse for the 3
degree observation. Then tan 3=h/x, or h=x(tan 3)
Having moved 700 ft. closer for the 5 degree
observation, tan 5=h/ (x-700), or h=(tan 5)(x-700)
We can now say x(tan 3)=(tan 5)(x-700)
x(0.05421)=(0.06749)(x-700)
.05421x=.06749x-47.24
-.01508x= -47.24
x=164.18 ft.
To the nearest tenth, 164.2 ft.
Problem 3.
Again, a diagram, and the same idea for solving as
in Problem 2.
Let the building height be x.
Let the distance of the observation point to the building be d
tan 40=(46+x)/d, so d=(46+x)/tan 40
tan 32=x/d, so .........d=x/tan 32
We thus have
(46+x)/tan 40=x/tan 32
(46+x)/(.83910)=x/.62487
x=(46+x)(.62487)/ .83910
.83910x=28.74+ .62487x
.83910x-.62478x=28.74
.21423x=28.74
x=28.74 / .21423
x=131.82ft.
To the nearest foot, 132
There now, that wasn't so bad, was it! Cheers
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The Path Between the Seas: The Creation of the Panama Canal, 1870-1914 List Price: $20.00 Sale Price: $8.89  |
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On December 31, 1999, after nearly a century of rule, the United States officially ceded ownership of the Panama Canal to the nation of Panama. That nation did not exist when, in the mid-19th century, Europeans first began to explore the possibilities of creating a link between the Atlantic and Pacific oceans through the narrow but mountainous isthmus; Panama was then a remote and overlooked part of Colombia... |
