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svp [43]
3 years ago
9

PLEASE HELP ME!!!!

Mathematics
1 answer:
Damm [24]3 years ago
7 0

Answer:

  • sin C=h/a
  • substitution property of equality
  • commutative property of multiplication

Step-by-step explanation:

Because two points determine a line, you can draw altitude​ BD perpendicular to AC with height h. By the definition of a sine ratio, <u>sin(C) = h/a</u>, which can be rearranged into​ a·sin(C) = h​. The area of △ABC is A=1/2bh. The <u>substitution property of equality</u> can be used to write A=1/2b(a sinC), which becomes A=1/2ab(sinC) by the <u>commutative property of multiplication</u>.

___

The mnemonic SOH CAH TOA reminds you that the sine ratio is ...

  Sin = Opposite/Hypotenuse

Here, the side of the right triangle opposite angle C is designated "h", the height of ∆ABC. The hypotenuse of that right triangle is side "a". So ...

  sin(C) = h/a

__

The substitution property of equality lets you replace any expression with its equal. Here, we have h=a·sin(C), so we can use a·sin(C) in place of h in the formula for triangle area:

  1/2bh = 1/2ba·sin(C)

__

The commutative property of multiplication lets you rearrange the order of the factors in a product, so ...

  ba = ab

and

  A = 1/2ba·sin(C) = 1/2ab·sin(C)

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