Consider the proof. Given: In △ABC, BD ⊥ AC Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A) Statement Reason 1. In △ABC, BD ⊥ AC 1. given 2. 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 multiplication 5. a2 = b2 – 2bx + c2 5. substitution 6. In △ADB, cos(A) = 6. def. cosine 7. ccos(A) = x 7. mult. prop. of equality 8. a2 = b2 – 2bccos(A) + c2 8. ? 9. a2 = b2 + c2 – 2bccos(A) 9. commutative property What is the missing reason in Step 8?
2 answers:
The missing reason is the following:
8. Substitute
is the equation of statement 5:
Solution: The missing reason in Step 8 is substitution of .
Explanation:
The given steps are used to prove the formula for law of cosines.
From step 5 it is noticed that our equation is
..... (1)
From step 7 it is noticed that the value of is .
So by substituting for in equation (1) we get the equation of step 8, i.e.,
Hence, the missing reason in Step 8 is substitution of .
You might be interested in
C 6*3=18 6*8= 48 and 3*8=24 24*48= 1152 1152/18=64
The product of 3 1/5 and 5/8 is 2.
Answer:
Alternate
Step-by-step explanation:
Because, as you can see, it is alternating
Answer:
The enlargement will be 30 ft by 7.5 ft.
Step-by-step explanation:
A scale drawing is a larger or smaller version of an object. To find the dimensions of the new drawing, multiply each measurement by the scale factor. The scale factor here is 5/2 or 2.5.
12(2.5)=30 ft
3(2.5)=7.5 ft