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Trigonometry vs. The Pythagorean Theorem
9
Transcript
Differences
Trigonometry
- depends on angle and side measures
- not used on right triangles
- calculator formulas: sine, cosine and tangent
The Pythagorean Theroem
- Formula: a^2 + b^2 = c^2
- defined right angle
- only able to find side legnths
- mainly uses square roots
Pythagoreon Theorem vs. Trigonometric ratios
Similarities
c
4
Pythagorean Theorem:
Find the value of C in the following figure.
Solution:
Let a = 4 cm and b = 12 cm
Apply the given values into the formula
a^2 + b^2 = c^2
42 + 122 = c^2
160 = c^2
c = 12.6
Trigonometry
First we must acess where x is in correlation to the other given numbers are.
Now that we know x is opposite the 40 degrees and adjacent to the 350ft, we can determine with trigonometry formula to use.
tan(x)= O/A is the correct formula.
Now we apply the formula and enter it in the calculator.
tan(40)= x/350
However we enter it in the calculator as 350*tan(40)
The outcoming answer is 293.69
12
x
40
350 ft.
- both dealing with triangles
- both can find a missing side
- angles can be used to determine missing side
Problems
Pythagorean Theorem and Trigonometry:
to find D we must use the Trigonometric ratio cosine
the equation is set up as cos(38)=d/300
set up on the calculator as 300cos38=d
236.4=d
To find h we must use the Pythagorean Theorem
a^2+b^2=c^2
236.4^2+h^2=300^2
55884.96+h^2=90000
h^2=34115.04
300
h
38
d
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