Given: in △abc, ad ⊥ bc prove: what is the missing statement in step 6? a. b = c b. h/b=h/c c. csin(b) = bsin(c) d. bsin(b) = csin(c)

Given: In ΔABC ,

To prove that:

          [Given]

In ΔADB

The sine angle is defined in the context of a right triangle is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle.

            [By definition of sine]                 .....[1]

Multiplication Property of equality states that you multiply both sides of an equation by the same number.

Multiply by c to both sides of an equation [1] we get;

Simplify:

                   ......[2]

Now, In ΔACD

Using definition of sine:

Multiply both sides of an equation by b;

      [Multiplication Property of equality]

Simplify:

                    ......[3]

Substitute [3] in [2];

             ......[4]

Division property of equality  states that if you divide both sides of an equation by the same nonzero number the sides remains equal.

[4] ⇒

Therefore, the missing statement in step 6 is;    

In step 6 we substitute the value we just found for h in step 5 into the equation in step 3. That's also an equation for h, so we're just setting the other sides equal:

Third choice.

this is a very good question

step-by-step explanation:

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