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ziro4ka [17]
3 years ago
5

Question 13 (1 point)

Mathematics
1 answer:
elixir [45]3 years ago
7 0

Answer:

yo u don't get wat u saying man

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Verify sine law by taking triangle in 4 quadrant<br>Explain with figure.<br>​
Ksivusya [100]

Proof of the Law of Sines

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

a

 sin  A

=

b

 sin  B

=

c

 sin  C

For more see Law of Sines.

Acute triangles

Draw the altitude h from the vertex A of the triangle

From the definition of the sine function

 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

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

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

c

 sin  C

=

a

 sin  A

Combining (4) and (5) :

a

 sin  A

=

b

 sin  B

=

c

 sin  C

- 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.

First the interior altitude. This is the same as the proof for acute triangles above.

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

 sin  C

Combining (4) and (9):

a

 sin  A

=

b

 sin  B

=

c

 sin  C

7 0
3 years ago
What would you Estimate 0.49
love history [14]

Answer:

. 50

Step-by-step explanation:

You would round to the closest number

. 49 is closer to. 50 than. 40

5 0
3 years ago
Read 2 more answers
what is the probability of drawing two blue cards if the first card is not included in the second draw? simplify your answer com
BlackZzzverrR [31]

Answer:

5/14

Step-by-step explanation:

The total number of cards is 8

There are 5 blue cards

P(1st card is blue) = blue/total = 5/8

We take away a blue card

The total number of cards is 7

There are 4 blue cards

P(2nd card is blue) = blue/total = 4/7

The probability of blue blue is P(blue blue ) =

P(1st card is blue)*P(2nd card is blue) =

5/8* 4/7

20/56

We can divide the top and bottom by 4

5/14

3 0
3 years ago
The sum of two numbers is 24 and their difference is 2. What are the numbers?
Musya8 [376]
Its 4 and 6
4 X 6= 24 
6-4= 2


8 0
3 years ago
Read 2 more answers
Solve 2(a + 7) = 5a - 13
timurjin [86]

Answer:

a = 9

Step-by-step explanation:

2(a + 7) = 5a - 13

We want to bring a to one side, I will choose to bring it to the right

First, expand the bracket by multiplying 2 with a + 7

2a + 14 = 5a - 13

Bring the -13 to the left by adding 13 to both sides

2a + 14 + 13 = 5a - 13 + 13

Simplify

2a + 27 = 5a

Bring the 2a to the right by subtracting 2a from both sides

2a - 2a + 27 = 5a - 2a

Simplify

27 = 5a - 2a

27 = 3a

Bring the 3 to the left by dividing both sides by 3

27÷3 = a

Simplify

a = 9

4 0
3 years ago
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