98 points will give brainliest to whoever shows given oblique △abc (image attached below) use the properties of right triangles and △abc to prove the law of sines. find the length of bc, rounded to the nearest tenth of a unit. in your final answer for parts a and b, include all of the necessary steps and calculations.

a) see proof below

b) BC = 23.7

Step-by-step explanation:

ABD is a right triangle

so sin A = opposite/ hypotenuse

 sin A = BD /c

Solving for BD by multiplying each side by c

c sin A = DB

BCD is  a right triangle

so sin C  = opposite/ hypotenuse

 sin C = BD /a

Solving for BD by multiplying each side by a

a sin C = BD

Setting BD = BD

c sin A = a sin C

Divide each side by c

c sin A     a sin C

   =  

 c                   c

sin A     a sin C

   =  

 1                   c

Now divide each side by a

sin A        a sin C

   =  

 a                a*   c

sin A         sin C

   =  

 a                   c

b find BC

A =46,  C = 31  and c =17

sin 46         sin 31

   =  

 a                   17

Using cross products

17 sin 46 = a sin 31

Divide each side by sin 31

17 sin 46/sin 31 = a sin 31/sin 31

17 sin 46 / sin 31 = a

23.7434419=a

Round to the nearest tenth

a= 23.7

BC = 23.7

a. & b. combined

The law of sines says that side a/the sine of angle A = side b/the sine of angle B = side c/the sine of angle C.  

You can prove this by using triangle ABC and sides a, AC, and c. For this problem, side AC = b.

        a                   b                17

= =

   sin 46°         sin 103°       sin 31°

(Next bold part is part b.)

      a                   17                                                                    

= (cross multiply and divide by sin 31°)  

   sin 46°          sin 31°                            

a = 23.7                                                                                                                                                                                       

       b                  17

= (cross multiply and divide by sin 31°)

 sin 103°         sin 31°

b = 32.2

    23.7                   ___

= 32.9 or 33  |

  sin 46°                       |

                                     |

   32.2                          |

= 33               > 33 = 33 = 33: Proof for the Law of Sines.

sin 103°                        |  

                                     |

    17                              |

= 33           ___  

 sin 31°

Hope this helps!

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.

y-y1=m(x-x1)

y-1=1(x-8)