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Which is an expression for the area of △ABC?

Which is an expression for the area of △ABC?-example-1

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9514 1404 393

Answer:

(C)

Explanation:

The law of sines tells you ...

AB/sin(C) = AC/sin(B)

AB = AC·sin(C)/sin(B)

The area of the triangle in terms of sides and angles is ...

Area = (1/2)AB·AC·sin(A)

Using the above expression for AB and filling in values, we get ...

Area = (1/2)AC·sin(C)/sin(B)·AC·sin(A)

Area = 15·sin(67°)/(2·sin(65°))·15·sin(48°) . . . . . . matches choice C

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