MATH SOLVE

6 months ago

Q:
# Consider the proof.Given: In △ABC, BD ⊥ ACProve: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A)StatementReason1. In △ABC, BD ⊥ AC 1. given2. In △ADB, c2 = x2 + h2 2. Pythagorean thm. 3. In △BDC, a2 = (b – x)2 + h2 3. Pythagorean thm. 4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication5. a2 = b2 – 2bx + c2 5. substitution6. In △ADB, cos(A) = 6. def. cosine7. ccos(A) = x 7. mult. prop. of equality8. a2 = b2 – 2bccos(A) + c2 8. ?9. a2 = b2 + c2 – 2bccos(A) 9. commutative propertyWhat is the missing reason in Step 8? a. Pythagorean theoremb. definition of cosinec. substitutiond. properties of multiplication

Accepted Solution

A:

C. Substitution

substituting 2bx for 2bccos(a)

substituting 2bx for 2bccos(a)