Question

PLEASE HELP ME!!!!

Because two points determine a line, you can draw altitude​BD⎯⎯⎯⎯ 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

Answer 1

Other user is correct

Explanation:

Answer 2

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

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)