Because two points determine a line, you can draw altitudeBD⎯⎯⎯⎯ perpendicular to AC⎯⎯⎯⎯⎯ with height h. By the definition of a sine ratio,_, which can be rearranged into a sinC=h. The area of △ABC is A=1/2bh. The _ can be used to write A=1/2b(a sinC), which becomes A=1/2ab(sinC) by the _.

Choices: sin C=h/a, sin c=a/h, symmetric property of equality, transitive property of equality, substitution property of equality, associative property of equality, distributive property of equality, and 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, sin(C) = h/a, which can be rearranged into a·sin(C) = h. The area of △ABC is A=1/2bh. The substitution property of equality can be used to write A=1/2b(a sinC), which becomes A=1/2ab(sinC) by the commutative property of multiplication.

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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

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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)

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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)

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

x equals 1

step-by-step explanation:

f(4)=f(×)

x=1