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
Answer:
Side AC which was labelled as "x" is 35 feet
Step-by-step 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
