SOLUTION: Avra is building a triangular dog run in her back yard. She makes a model of the dog run by drawing △ABC, where AB=20 feet, AC=40 feet, and m∠A=46.6°.
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Question 1062983: Avra is building a triangular dog run in her back yard. She makes a model of the dog run by drawing △ABC, where AB=20 feet, AC=40 feet, and m∠A=46.6°.
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Inside the dog run, Avra wants to install sod that costs $0.79 per square foot. How much money should she expect to spend on sod when she goes to the hardware store?
Avra should expect to spend $__________.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
We will use the law of cosines to get the length of side BC and then use Heron's formula to get the area of triangle ABC
:
BC^2 = 20^2 + 40^2 - 40*20*cos(46.6) = 1450.33
:
BC = 38.0832
:
s = (40 +20 +38.0832) / 2 = 49.0416
:
area of ABC = sqrt(49.0416*(49.0416-20)*(49.0416-40)*(49.0416-38.0832))
:
area of ABC = 375.6547 square feet
:
total cost = 375.6547 * 0.79 = 296.7672
:
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Avra should expect to spend $296.77
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