32 - 34 Maxima and minima problems of a rectangle inscribed in a triangle

Problem 32
Find the dimension of the largest rectangular building that can be placed on a right-triangular lot, facing one of the perpendicular sides.

Problem 33
A lot has the form of a right triangle, with perpendicular sides 60 and 80 feet long. Find the length and width of the largest rectangular building that can be erected, facing the hypotenuse of the triangle.

Problem 34
Solve Problem 33 if the lengths of the perpendicular sides are a, b.

21 - 24 Solved problems in maxima and minima

Problem 21
Find the rectangle of maximum perimeter inscribed in a given circle.

Problem 22
If the hypotenuse of the right triangle is given, show that the area is maximum when the triangle is isosceles.

Problem 23
Find the most economical proportions for a covered box of fixed volume whose base is a rectangle with one side three times as long as the other.



The Six Trigonometric Functions

  1. $\sin \theta = \dfrac{a}{c}$
  2. $\cos \theta = \dfrac{b}{c}$
  3. $\tan \theta = \dfrac{a}{b}$
  4. $\csc \theta = \dfrac{c}{a}$
  5. $\sec \theta = \dfrac{c}{b}$
  6. $\cot \theta = \dfrac{b}{a}$