Page 69 - Calculating Agriculture Cover 20191124 STUDENT - A
P. 69
CH 5] Calculating Agriculture 5-7
Example C: What is the perimeter of a triangle whose sides measure c
5 inches, 7 inches, and 10 inches? a
Solution: P = 5 + 7 + 10 = 22 inches
b
Calculating the side lengths of a triangle — Pythagorean equation.
All triangles have three sides, and the three angles of any triangle, when summed,
o
o
equal 180 whereas the sum of the angles in a square equal 360 .
The sides of a right triangle are identified as a=height, b=base, and c=hypotenuse.
Any one side of any triangle can be calculated starting with the equation:
2
2
2
a + b = c
where a, b and c are the length of each respective side. This equation is read as “a
squared plus b squared equals c squared.” The exponent 2 causes the value of any
side to be multiplied by itself as in ‘a x a = a ’. Thus if “a” has a value of 3, then a is:
2
2
2
a = a x a
2
a = 3 x 3 = 9
From this equation an unknown length of any side of can be calculated as long as the
lengths of the other two sides are known.
Example: A triangle with side a = 15 and side b=6, calculate side c, and round
your answer to the thousandths, three digits to the right of the
decimal.
Solution algorithm:
2
2
Triangle equation: a + b = c 2
5
2
2
2
15 + 6 = c
2
(15 x 15) + (6 x 6) = c
Now you need to calculate the square root ( √ )of
2
225 + 36 = c 261. It is easily found by tapping the square root
symbol on your calculator √ ; and we determine
261 = c 2 that the calculator reports the square root of
√261 = 16.155. Thus the value of side c in our
c = √c 2 triangle is 16.155. c = 16.155
√261 = √c 2
16.155 = c
Calculating square root algorithm ( √ ). Calculating square root of a number
is a function of division and as such can be accomplished with paper and pencil with
this algorithm, and we shall use the answer from our previous Example for clarity and
round to the 1000ths (three digits to the right of the decimal). You will note that this
algorithm has qualities similar to division, but also requires using test divisors.
Example A: Calculate the square root of 261.
Solution algorithm:
1) Place the decimal point directly over the decimal point in the number.
.
√ 261 = √ 261 .
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