Figure 3.6.2 shows an acute triangle with angles A, B, and C and opposite sides a, b,
Question:
Figure 3.6.2 shows an acute triangle with angles A, B, and C and opposite sides a, b, and c. By dropping a perpendicular from each vertex to the opposite side, derive the equations
Regarding these as linear equations in the unknowns cosA, cosB, and cosC, use Cramer’s rule to derive the law of cosines by solving for
Thus
a2 = b2 + c2 - 2bc cosA.
Note that the case A = π/2 (90°) reduces to the Pythagorean theorem.
Transcribed Image Text:
c cos B + bcos C = a c cos A + a cos C = b a cos B + bcos A = c.
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Related Book For
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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