Find the numerical value of the log expression. log a = 11 log b = -5 log c= 6
1 answer:
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Answer: the length of one leg is 30 inches and the leg of the other leg is 16 inches.
Step-by-step explanation:
Let the other leg of the triangle be x inches.
One leg of the triangle is 14 inches less than the other leg. This means that the length of this leg of the triangle is (x-14) inches.
The length of the hypothenuse of the right triangle is 34 inches.
The diagram of the triangle, showing it's dimensions is shown in the attached photo.
Applying Pythagoras theorem,
Hypothenuse^2 = adjacent^2 + opposite ^2
The simplified equation that can be used to find the lengths of the legs is
34^2 = (x-14)^2 + x^2
1156 = (x-14)(x-14) + x^2
1156 = x^2 - 14x - 14x + 196 + x^2
1156 = 2x^2 -28x +196
2x^2 -28x +196 - 1156 = 0
2x^2 -28x - 960 = 0
Dividing through by 2,
x^2 -14x - 480 = 0
x^2 +16x - 30x - 480 = 0
x(x+16)-30(x+16) = 0
(x + 16)(x - 30) = 0
x+16 = 0 or x-30= 0
x = -16 or x = 30
So x = 30 inches( because it cannot be negative)
One leg = x-14 = 30-14 = 16 inches
