It is given that in △ABC, AD ⊥ BC. Using the definition of sine with angle C in △ACD results in sin (C) =. Using the multiplication property of equality to isolate h, the equation becomes bsin (C) = h. Knowing that the formula for the area of a triangle is A = bh is and using the side lengths as shown in the diagram, which expression represents the area of △ABC? bsin (C) absin (C) cbsin (C) hbsin (C)

Question

Mathematics

Rihanna Schmitt

29 November, 03:25

It is given that in △ABC, AD ⊥ BC. Using the definition of sine with angle C in △ACD results in sin (C) =. Using the multiplication property of equality to isolate h, the equation becomes bsin (C) = h. Knowing that the formula for the area of a triangle is A = bh is and using the side lengths as shown in the diagram, which expression represents the area of △ABC? bsin (C) absin (C) cbsin (C) hbsin (C)

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Answers (1)

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Kelsey Zavala · Answer 1

We see here in the diagram that the base is a. We know this because the height is perpendicular to it. We also know the height is bsin (C) which, when replace h for bsin (C) and a for the base, we get A=absin (C), which is the second option.