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Lapatulllka [165]
3 years ago
10

15. A plane flies 35 miles east and 80 miles south of an airport. The pilot

Mathematics
1 answer:
Alexxandr [17]3 years ago
4 0

The opposite of East is West.

The opposite of South is North.

He would need to fly North West

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Verify sine law by taking triangle in 4 quadrant<br>Explain with figure.<br>​
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Proof of the Law of Sines

The Law of Sines states that for any triangle ABC, with sides a,b,c (see below)

a

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=

b

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For more see Law of Sines.

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Draw the altitude h from the vertex A of the triangle

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Repeat the above, this time with the altitude drawn from point B

Using a similar method it can be shown that in this case

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a

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- Q.E.D

Obtuse Triangles

The proof above requires that we draw two altitudes of the triangle. In the case of obtuse triangles, two of the altitudes are outside the triangle, so we need a slightly different proof. It uses one interior altitude as above, but also one exterior altitude.

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Draw the altitude h from the vertex A of the triangle

 sin  B =

h

c

      a n d          sin  C =

h

b

or

h = c  sin  B       a n d         h = b  sin  C

Since they are both equal to h

c  sin  B = b  sin  C

Dividing through by sinB and then sinC

c

 sin  C

=

b

 sin  B

Draw the second altitude h from B. This requires extending the side b:

The angles BAC and BAK are supplementary, so the sine of both are the same.

(see Supplementary angles trig identities)

Angle A is BAC, so

 sin  A =

h

c

or

h = c  sin  A

In the larger triangle CBK

 sin  C =

h

a

or

h = a  sin  C

From (6) and (7) since they are both equal to h

c  sin  A = a  sin  C

Dividing through by sinA then sinC:

a

 sin  A

=

c

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Combining (4) and (9):

a

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=

b

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=

c

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vekshin1

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