A land surveyor was measuring the distances from various points on a plot of land. Her measuring tool broke before the last leg measure was determined.

Right triangle A B C. Side A C is x, side A B is 12 feet, and hypotenuse B C is 37 feet.

The unknown length can be found using the Pythagorean theorem.

The theorem states that the of the squares of the legs is the square of the hypotenuse.

The missing length is feet.

The theorem states that the sum of the squares of the legs is the square of the hypotenuse.

The missing length is 35 feet.

Step-by-step explanation: As stated in the Pythagoras theorem quoted above, the square of the longest side which is the hypotenuse equals to the sum of the squares of the two other sides which can be expressed as follows;

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse and AB and BC are the other two sides. In our question, the hypotenuse is given as BC while the other two sides are AC and AB, hence the formula becomes,

BC^2 = AB^2 + AC^2

37^2 = 12^2 + AC^2

1369 = 144 + AC^2

Subtract 144 from both sides of the equation

1225 = AC^2

Add the square root sign to both sides of the equation

35 = AC

Therefore the missing length is 35 feet

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