Question

PLEASE HELP!! FILL IN THE BLANK MATH QUESTION, ONLY ANSWER IF YOU KNOW THE CORRECT ANSWER CAUSE MY GRADE DEPENDS ON IT

Answer 1

First blank: sin. C = h/a
The ratio for sin. is opposite (the height) over hypotenuse (a).

Second blank: Area = (1/2)b(a sin. C)
In this substitution, we are substituting the value of h into the traditional area of a triangle formula.

Third Blank: Area = (1/2)ab(sin C)
We are using the commutative property to move the position of a. 
Hope this helps and good luck in your classes!

Answer 2

The altitude of the triangle would be another line added to the triangle which bisects angle B. We are calling this side h. Looking at the right triangle this added side forms, with respect to angle C, "h" would be the opposite side and "a" would be  the hypotenuse. We know that sin∅ = opposite/hypotenuse, so the first blank is:

sinC = h/a

For the second blank, we need to redefine side h. We know sinC = h/a, so let's rearrange that to solve for h:

h = a*sinC

If we substitute a*sinC for h is 0.5*b*h, we get:

Area = 1/2 * b(asinC)

Finally, according to the commutative property of multiplication, the order of terms being multiplied doesn't matter. Therefore the final blank is:

Area = 1/2 * ab(sinC)