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S_A_V [24]
3 years ago
9

A+B-C=3pi then find sinA+sinB-sinC

Mathematics
1 answer:
steposvetlana [31]3 years ago
7 0
The answer:
the full question is as follow:

if A+B-C=3pi, then find sinA+sinB-sinC

first, the main formula of sine and cosine are:
sinC = 2sin(C/2)cos(C/2)
sinA +sinB = 2sin[(A+B)/2]cos[(A-B)/2]

therefore: 
 sinA+sinB-sinC = 2sin[(A+B)/2]cos[(A-B)/2] - 2sin(C/2)cos(C/2)

sin[(A+B)/2] = cos(C/2)
2sin(C/2)cos(C/2) = cos[(A+B)/2
and 
A+B-C=3 pi implies A+B =3 pi + C, so 
cos[(A+B)/2] = cos [3 pi/2  + C/2]
and  with the equivalence cos (3Pi/2  + X) = sinX

sinA+sinB-sinC =  cos(C/2)+ sin(C/2) 
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The base of a triangle is 4 cm greater than the
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Answer:

Step-by-step explanation:

Formula for area of a triangle:

Height x Base /2

Base (b) = h +4

Height = h

h + 4 x h /2 = 30cm

=> h +4 x h = 60

=> h+4h =60

=> 5h = 60

=> h = 12

Height = 12

Base = 12 +4 = 16

4 0
3 years ago
A shipping company damaged 15 packages. Each package was valued at $175.50. Which expression represents this situation?
Allushta [10]

Answer: A

Step-by-step explanation:

15 packages damaged. Cost is -175.50 this is a loss. So 15x(-175.50)

3 0
3 years ago
What percent of 500 is 50?​
mestny [16]

Answer:50/500×100=10%

Therefore, 10% of 500 is 50.

Hope this answer helps you...

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
The larger of two numbers is 15 more than three times the smaller number. If the sum of the two numbers is 63, find the numbers
Amanda [17]

Answer:

The smaller number equals 12, the larger number equals 51.

Step-by-step explanation:

x + (3x + 15) = 63

Combine like terms.

4x + 15 = 63

Subtract 15 from both sides.

4x + (15 -15) = (63 - 15)

4x = 48

Divide both sides by 4.

4x/4 = 48/4

x = 12

Check answer.

12 + (3(12) + 15) = 63

12 + 36 + 15 = 63

63 = 63

7 0
3 years ago
In a right triangle one leg measures a quarter of the other, how much do its acute angles measure? with procedure please​
KATRIN_1 [288]

Answer:

The answer to your question is 14° and 76°

Step-by-step explanation:

Data

leg 1 = x

leg 2 = x/4

angle 1 = ?

angle 2 = ?

Process

To solve problem use trigonometric functions. We must use the trigonometric function that relates both legs (tangent).

    tangent Ф = Opposite side / Adjacent side

-Substitution

    tan Ф = (x/4) / x

-Simplification

    tan Ф = x / 4x

    tan Ф = 1/4

-  Find Ф

     Ф = tan⁻¹(1/4) =  14°

- Find the other acute angle

  The sum of the internal angles in a triangles equals 180°

       Ф + Ф₁ + 90° = 180

-Solve for Ф₁

        Ф₁  = 180 - 90 - 14

-Result

        Ф₁ = 76°              

3 0
3 years ago
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