A retractable awning above a patio lowers at an angle of 50

A retractable awning above a patio lowers at an angle of 50° from the exterior wall at a height of y = 11 feet above the ground (see figure). No direct sunlight is to enter the door when the angle of elevation of the sun is greater than 70°. What is the length x of the awning? (Round your answer to two decimal places.) x = ?ft

Solution

Solution

              To   find   the length x   of   the swing

             Let the base of the wall be A, the pivot point of the awning (10\' above A) be B

             and CA is the line from A to the end of the awning such that BAC = 20

            As BAC = 50   then ACB = 110 .

            By the Sine Rule, AC/Sin20 = AB/Sin110
            Thus,    AC = ABSin20/Sin110

                         = 10 x 0.34202 / 0.93969

                             = 3.6397 ft (4dp)

           The required length of the awning   is   3.64 ft