install a flag pole of height 10.0 m at the south end of one of the outdoor pools, which lies along a north–south axis.

You are working at your university swimming center. The athletic department decides that it would like to install a flag pole of height 10.0 m at the south end of one of the outdoor pools, which lies along a north–south axis. The pool is 3.00 m deep and the flag pole is to be installed 4.00 m from the south edge of the pool, midway along the length of the south edge. (a) Your supervisor knows of your expertise in physics and asks you to determine the distance of the shadow of the tip of the flag pole on the bottom of the pool from the south wall of the pool on a summer day when the Sun appears directly south and at an angle of 65.08 above the horizon. (b) Your supervisor also asks if there is any time during the year that the flag pole will not cast a shadow along the bottom of the pool when the Sun is due south. The highest the Sun reaches in the sky at this location is 68.58 at the summer solstice.