In the following problem the engineer must find out the shorter leg of this right angle triangle. The Engineer has two
options, the ancronym **SOHCAHTOA** or an easier route known as **Pythagorean Theorem**

In the problem it is defines that

2 2 2

C =A + B

2 2 2

36 =22 + B

2

1296=484 + B

2

B =1296-484

2

B = 812

Than we find the square root of 812 in order to find out what **B** will equal.

Square root of 812=28.495

__B=28.495__

Now if the leg of the of the triangle was not known than we would have to apply trigonometric functions

**SOHCAHTOA**

Allows us to remember how to apply the sine, cosine or tangent to this equation.

So I'm going to choose sine in order to find out how long of a side I need to complete the triangle.

Sin40=__X__

36

0.6428=X/36

36[0.6428=X/36]

23.14=36X/36

X=23.14 36X/36
the 36's cancel each other leaving

X

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Now it may be apparent that the two awnsers are varied from eachother. This is because two equations were used in each
and many numbers are rounded throughout the sequence. This loss of perfection leaves the awnsers flawed so in applying equations
to Civil engineering the slighest error may spell tragedy.