Question

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.

Answer 1

Side AC which was labelled as "x" is 35 feet

Explanation:

In mathematics, the Pythagorean theorem , also known as

Pythagoras' theorem , is a fundamental relation in Euclidean

geometry among the three sides of a right triangle. It states that the

area of the square whose side is the hypotenuse (the side opposite

the right angle ) is equal to the sum of the areas of the squares on

the other two sides. This theorem can be written as an equation

relating the lengths of the sides a, b and c, often called the

"Pythagorean equation":[1]

where c represents the length of the hypotenuse and a and b the

lengths of the triangle's other two sides. The theorem, whose history

is the subject of much debate, is named for the ancient Greek thinker

Pythagoras.

It is stated below

a² + b² = c²

For the question given,Right triangle A B C with Side A C is x, side A B is 12 feet, and hypotenuse B C is 37 feet.We are now asked to find the foot of the triangle or the base.

Side AC is "a",side AB is "b" and side BC is "c"

a² + b² = c²

but since we do not know "a",we make it the subject of the formula

a = √(c² - b²)

a = √(1369 - 144)

a = √1225

a = 35

Therefore,Side AC which was labelled as "x" = 35 feet

Answer 2

Answer: 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