Geometry/Chapter 15

If you understand the Pythagorean Theorem and what it derives from, you can now start applying its formula to everyday problems.

Examples

Example 1 - Plane Distance

A plane flies south from an airport at 300 miles per hour. Another plane flies out at the same time due east at 250 miles per hour. How far apart are the planes after three hours?

Solution to Example 1

The solution would be about 1172 miles apart after three hours. How do we determine the answer?

 $a^{2}+b^{2}=c^{2}$                          The Pythagorean Theorem.
 $(300*3)^{2}+(250*3)^{2}=c^{2}$                Substituting miles per hour.
 $900^{2}+750^{2}=c^{2}$                       Simplifying.
 $810000+562500=c^{2}$                   Simplifying.
 ${\sqrt {c^{2}}}={\sqrt {810000+562500}}$      Finding the hypotenuse (or distance).
 $c={\sqrt {1372500}}$ or $c\approx 1172$     Our distance, simplified.

Navigation

• Geometry Main Page
• Motivation
• Introduction
• Geometry/Chapter 1 - HS Definitions and Reasoning (Introduction)
  • Geometry/Chapter 1/Lesson 1 Introduction
  • Geometry/Chapter 1/Lesson 2 Reasoning
  • Geometry/Chapter 1/Lesson 3 Undefined Terms
  • Geometry/Chapter 1/Lesson 4 Axioms/Postulates
  • Geometry/Chapter 1/Lesson 5 Theorems
  • Geometry/Chapter 1/Vocabulary Vocabulary
• Geometry/Chapter 2 Proofs
• Geometry/Chapter 3 Logical Arguments
• Geometry/Chapter 4 Congruence and Similarity
• Geometry/Chapter 5 Triangle: Congruence and Similiarity
• Geometry/Chapter 6 Triangle: Inequality Theorem
• Geometry/Chapter 7 Parallel Lines, Quadrilaterals, and Circles
• Geometry/Chapter 8 Perimeters, Areas, Volumes
• Geometry/Chapter 9 Prisms, Pyramids, Spheres
• Geometry/Chapter 10 Polygons
• Geometry/Chapter 11 $\mathbb {R} ,\mathbb {R} ^{2},\mathbb {R} ^{3}$
• Geometry/Chapter 12 Angles: Interior and Exterior
• Geometry/Chapter 13 Angles: Complementary, Supplementary, Vertical
• Geometry/Chapter 14 Pythagorean Theorem: Proof
• Geometry/Chapter 15 Pythagorean Theorem: Distance and Triangles
• Geometry/Chapter 16 Constructions
• Geometry/Chapter 17 Coordinate Geometry
• Geometry/Chapter 18 Trigonometry
• Geometry/Chapter 19 Trigonometry: Solving Triangles
• Geometry/Chapter 20 Special Right Triangles
• Geometry/Chapter 21 Chords, Secants, Tangents, Inscribed Angles, Circumscribed Angles
• Geometry/Chapter 22 Rigid Motion
• Geometry/Appendix A Formulae
• Geometry/Appendix B Answers to problems
• Appendix C. Geometry/Postulates & Definitions
• Appendix D. Geometry/The SMSG Postulates for Euclidean Geometry