Today, 4 cows produced 26 gallons of milk. If each cow produced the same amount of milk, how many gallons of milk did each cow p
2 answers:
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Answer: Area of ΔABC is 2.25x the area of ΔDEF.
Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as
with a as side of the triangle.
Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:
a₁ = 1.2a
Then, its area is
Triangle DEF is 20% smaller than the original, which means its side is:
a₂ = 0.8a
So, area is
Now, comparing areas:
2.25
<u>The area of ΔABC is </u><u>2.25x</u><u> greater than the area of ΔDEF.</u>
Answer:
27 degrees
Step-by-step explanation:
The easy way is by remembering the formula (a-b)/2=c, where a is the larger angle, and b is the smallest angle. (90-36)/2=27.
The longer, more drawn out answer goes as follows. See the image to understand the notation I use:
- AOE + BOD + BOA + DOE = 360
- AOE + BOD = 90 + 36 = 126
- BOA + DOE = 360 - AOE - BOD = 234
- Since the sum of a triangle's angles is 180, ODE = (180 - DOE) / 2
- Likewise, OBA = (180 - BOA) / 2
- Since CDE is 180, CDO = 180 - ODE = 180 - (180 - DOE) / 2
- Likewise, CBA is 180, so CBO = 180 - OBA = 180 - (180 - BOA) / 2
- The interior angles of the irregular polygon CBOD add up to 360, so CBO + CDO + BOD + BCD = 360.
- Substituting what we already found, 180 - (180 - BOA)/2 + 180 - (180 - DOE)/2 + 36 + BCD = 360
- Cleaning it all up, we get 180 + (BOA + DOE)/2 + 36 + BCD = 360
- As we found in line 3, BOA + DOE = 234, so substituting that in, 180 + 117 + 36 + BCD = 360
- Finally, solving for BCD (360 - 36 - 117 - 180) we get our answer, 27
Note: The long drawn out method shown above is a way to derive the formula for the secant theorem. You do not need to use this method every time. Just remember, large angle minus small angle, all divided by 2. That is it.
