The figure shows Angel Stadium of Anaheim and the triangle formed by home plate, the right center field fence, and third base. In the figure, the approximate distance from the right center field fence to third base is 339.4 ft.
Outline a plan for how you are going to determine the distance x from home plate to the right center field fence.
Implement your plan. Show all of your work and round your answer to the nearest tenth of a foot
Use Law of Sines as follows:
Sin(63.4) / 339.4 =Sin(right center) / 90
0.894154 /339.4 =Sin(right center) / 90 cross multiply
80.474 = 339.4 x sin(right center) divide both sides by 339.4
0.23711 = sin(right center)
Right center angle =arcsin(0.23711)
Right center angle =13.716 degrees
180 - [63.4 + 13.716] =102.884 degrees - the angle at 3rd base.
x / sin(102.884) = 339.4 / sin(63.4)
x / 0.974823 = 339.4 / 0.894154 cross multiply
0.894154x =330.855 divide both sides by 0.894154
x =~370 feet - the length of x