Asteep mountain is inclined 72 degree to the horizontal and rises 4300 ft above the surrounding plain. a cable car is to be installed by connecting a cable from the top of the mountain to a spot on the plain that is 800 ft from the base of the mountain. find the shortest length of cable needed.

A3cm×3cm\greend{3\,\text{cm} \times 3\,\text{cm}} 3cm×3cm start color greend, 3, space, c, m, times, 3, space, c, m, end color greend rectangle sits inside a circle with radius of 4cm\blued{4\,\text{cm}} 4cm start color blued, 4, space, c, m, end color blued . what is the area of the shaded region? round your final answer to the nearest hundredth.