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cassie2021
04.02.2020 •
English
Aroom in the shape of a triangle has sides of length 7 yd, 8 yd, and 11 yd. if carpeting costs $17.50 a square yard and padding costs $3.25 a square yard, how much to the nearest dollar will it cost to carpet the room, assuming that there is no waste?
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Ответ:
where s is the semi-parameter of the triangle with sides a, b and c
So,
So, the total cost of carpeting the room is,
$579.5
Ответ:
Using the Law of Cosines:
cos(A) = (b² + c² - a²)/2bc = [(8)² + (11)² - (7)²)/2(8)(11) = 0.773
A = acos(0.773) = 39.4°
Using the Law of Sines:
sin(A)/a = sin(B)/b ==> sin(B) = (b/a)sin(A) = (8/7)sin(39.4°) = 0.725
B = asin(0.725) = 46.5°
Knowing angles A and B, angle C is:
C = 180° - A - B = 180° - 39.4° - 46.5° = 94.1°
Finally, the area is:
Area = (ab/2)sin(C) = [(7)(8)/2]sin(94.1°) = 27.928 yd²
The total cost is (27.928)($17.50 + $3.25) = $579.51
Ответ: