The cross sections of an irrigation canal are isosceles trapezoids of which three sides are 8 feet long (see figure). Determine the angle of elevation of the sides such that the area of the cross sections is a maximum by completing the following.

(a) Analytically complete six rows of a table such as the one below. 

(b) Use a graphing utility to generate additional rows of the table. Use the table to estimate the maximum cross-sectional area.

(c) Write the cross-sectional area A as a function of .

(d) Use calculus to find the critical number of the function in part (c). Then find the angle that will yield the maximum cross-sectional area. What is the maximum area?

(e) Use a graphing utility to graph the function in part (c) and verify the maximum cross-sectional area.

Transcribed Image Text:

10° 20° Base 1 8 8 Base 2 Altitude 8 + 16 cos 10° 8 sin 10° 8 sin 20° 8 + 16 cos 20° Area = 22.1 42.5