Sarah and kelvin are calculating the area of a circle with a radius of 52cm kelvin ises 3.14 for pi when calculating this area while sarah uses the pi button on her calculator kevin gets a soloution of 8,490.56 cm2 and sarah gets a soloution of 8,494.87 cm2

The sum of angles in ΔABD is ...

  2a + b + d = 180

The sum of angles in ΔAHG is ...

  a + h + 90 = 180

Solving this second equation for a, we have ...

  a = 180 -90 -h = 90 -h

Substituting this into the first equation, we have ...

  2(90 -h) +b +d = 180

  180 -2h +b +d = 180 . . . . . eliminate parentheses

  b + d = 2h . . . . . . . . . . . . . add 2h-180

  h = (1/2)(b+d) . . . . . . . . . . divide by 2