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!

i don't know, but that looks pretty bad. my school passed us unless we failed in all the subjects, but idk abt ur school's rules.

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