PYTHAGOREAN THEOREM

PYTHAGOREAN THEOREM

Relationships:

This is used when one side of a right triangle is missing.

-       The square of the hypotenuse side is equal to the sum of the square of the other two sides.

 A theorem in geometry. The square of the length of the hypotenuse of a right triangle  equals the sum of the squares of the lengths of the other two sides.
    
      In most cases, especially in geometry, triangle has a real deal issues. This unique figure  have different types. Scalene, isosceles, right, etc.Getting the measure of its side is also  different. Only the right triangle owns the right to use the theorem called " Pythagorean  Theorem". It states that the square of the longest side is equal to the sum of the square of  the other two sides.

      Right triangle is a triangle one side measures 90 degrees. By this definition right triangle  differs from the all of other triangle. So we must be careful when using the Pythagorean  theorem by miss using the theorem to other types. The theorem cannot be apply to any  type of triangle except "Right Triangle".

Formula:

Square of hypotenuse = square of opposite side + square of adjacent side.

H ² = O ² + A ²

Where:

H = hypotenuse

O = opposite

A = adjacent

Illustration:

For triangle with angle A as reference angle.

For triangle with angle A as reference angle.

Problem:

1. A triangle has opposite side measures 3 inches and adjacent side measures 4 inches. Find the hypotenuse side of the triangle.

Illustration aids visualization.

Given:

O = 3 in.
A = 4 in.
H = ?

Required:

Hypotenuse (H).

Solution:

From the formula:

H ² = O ² + A ²

H ² = (3 in) ² + (4 in) ²

H ² = 9 in ² + 16 in ²

H ² = 25 in ²

H  = 5 in. (answer)

2. The triangle shown below has one side missing. What is the right Pythagorean theorem formula to use with this type of problem? Using the formula given, Find the length of the missing side.

Illustrated figure from the statement above.

Depending on the reference angle we will be the basis, we can use adjacent as the unknown side or we can assume opposite was the missing side. Any of the formula given is applicable. In this case, we will assume our reference angle is angle B, so our opposite side is the unknown. We can use the formula O² = H² – A^{2  .}

^Therefore:

Given:

O = ??
A = 4 m
H = 8 m

Required:
opposite (O).

Solution:

From the formula:

O² = H² – A² 

O² = 64 m² – 16 m² 

O² = 48 m² 

O =  6.928 m

The side missing has the measures 6.928 m.

Exercises:

Find the missing side of the given triangle.

1.    Solve for the value of x and write your answer here. Answer: ____________

2. Solve for the value of AB and write your answer here. Answer: ____________

      

3. Solve for the value of CB and write your answer here. Answer: ____________

Finding the triangle's side measure with Pythagorean need more little exposure to the problem. A constant practice is recommended. 

REFERENCES

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