Solving for Line FC Using the Pythagorean Theorem

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SUMMARY

The discussion focuses on solving for line FC using the Pythagorean Theorem, specifically the equation A² + B² = C². The user attempts to derive the length of line FC by analyzing a diagram and applying the relationship between the sides of right triangles. The calculation involves setting 1/2ac equal to bc, with bc given as 12, leading to the equation 16² + b² = c². Clarification is sought regarding the geometric configuration of the triangles involved.

PREREQUISITES
  • Understanding of the Pythagorean Theorem (A² + B² = C²)
  • Basic knowledge of right triangles and their properties
  • Ability to interpret geometric diagrams
  • Familiarity with algebraic manipulation of equations
NEXT STEPS
  • Review the properties of right triangles and the Pythagorean Theorem
  • Explore geometric interpretations of triangle configurations
  • Learn how to derive relationships between triangle sides in various configurations
  • Practice solving similar problems involving the Pythagorean Theorem
USEFUL FOR

Students studying geometry, mathematics educators, and anyone looking to strengthen their understanding of the Pythagorean Theorem and its applications in solving geometric problems.

Cyclopse
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Homework Statement


Find line FC in the given problem.
10zsm6b.jpg




Homework Equations


A^2 + b^2 = c^2



The Attempt at a Solution


according to the diagram,
1/2ac = bc - since the the two right triangles share the same hypotenuse.
bc = 12
so 1/2ac = 12,
i got the answer as 16^2 + b^2 = c^2,
is that correct?
 
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Hi Cyclopse! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif
Cyclopse said:
according to the diagram,
Is it intended that we regard ABCD as a rectangle? It isn't marked as such.
1/2ac = bc - since the the two right triangles share the same hypotenuse.
But you could construct many different right triangles all having the same length hypotenuse.
bc = 12
so 1/2ac = 12,
i got the answer as 16^2 + b^2 = c^2,
is that correct?
Can you express FC in meters?
 
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