13822 to 1 significant figure
1 answer:
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Answer:
When we know all 3 sides we use the law of cosines
a = 47
b = 11
c = 38
cos (A) = (b^2+c^2-a^2) / (2bc)
cos (A) = -0.7703349282
Angle A = 140.38
cos (B) = (a^2 + c^2 -b^2) / (2ac)
cos (B) = 0.9888017917
Angle B = 8.5826 degrees
cos (C) = (a^2 + b^2 -c^2) / 2ab
cos (C) = 0.8568665377
cos (C) = 31.033 degrees
Angle W would be the smallest angle so it equals
31.033 degrees or rounded to nearest tenth
31.03
Step-by-step explanation:
Let the length of second side be x" ,
So,
Length of first side = 2" shorter than second = ( x - 2 )"
Length of third side = 5" longer than second = ( x + 5 )"
=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=
Given, perimeter = 33"
= > first side + second side + third side = 33"
= > ( x - 2 ) + x + ( x + 5 ) = 33
= > x - 2 + x + x + 5 = 33
= > 3x + 3 = 33
= > 3x = 30
= > x = 10
Hence, length of each side is
First side = ( x - 2 )" = ( 10 - 2 )" = 8 inches
Second side = x " = 10 inches
Third side = ( x + 5 )" = ( 10 + 5 )" = 15 inches
So,
Length of first side = 2" shorter than second = ( x - 2 )"
Length of third side = 5" longer than second = ( x + 5 )"
=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=
Given, perimeter = 33"
= > first side + second side + third side = 33"
= > ( x - 2 ) + x + ( x + 5 ) = 33
= > x - 2 + x + x + 5 = 33
= > 3x + 3 = 33
= > 3x = 30
= > x = 10
Hence, length of each side is
First side = ( x - 2 )" = ( 10 - 2 )" = 8 inches
Second side = x " = 10 inches
Third side = ( x + 5 )" = ( 10 + 5 )" = 15 inches