An arbitrary point P is chosen on side BC of triangle ABC and perpendiculars PU and PV are drawn from P to the other two sides of the triangle. (It may be that U or V lies on an extension of AB or AC and not on the actual side of the triangle. This can happen, for instance, if angle A is obtuse and point P is very near B or C.) Draw the figure and explain why the sum PU+PV of the lengths of the two perpendiculars is constant as P moves along BC. In other words, this quantity is independent of the choice of P.
An arbitrary point P is chosen on side BC of triangle ABC and perpendiculars PU and PV are drawn from P to the other two sides of the triangle. (It may be that U or V lies on an extension of AB or AC and not on the actual side of the triangle. This can happen, for instance, if angle A is obtuse and point P is very near B or C.) Draw the figure and explain why the sum PU+PV of the lengths of the two perpendiculars is constant as P moves along BC. In other words, this quantity is independent of the choice of P.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.4: Trigonometric Functions
Problem 76E
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An arbitrary point P is chosen on side BC of triangle ABC and perpendiculars PU and PV are drawn from P to the other two sides of the triangle. (It may be that U or V lies on an extension of AB or AC and not on the actual side of the triangle. This can happen, for instance, if angle A is obtuse and point P is very near B or C.) Draw the figure and explain why the sum PU+PV of the lengths of the two perpendiculars is constant as P moves along BC. In other words, this quantity is independent of the choice of P.
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