4.22

OA = {-b, 0, 0}
OE = {(b/2), 0, 0}
OD = {0, 0, h}
OF = (1/2) (OA + OD)

EF = OF - OE

para1 = h -> Sqrt[l^2 - b^2]

para2 = b -> (a/(Sqrt[3]))

Simplify[Sqrt[EF  . EF] /. para1 /. para2]

4.23

p1 = {0, 0}
p2 = {100 Cos[θ], 
        100 Sin[θ]}
p3 = {x, y}
p4 = {250, 0}

p3max = 
      FindRoot[{(p3 - p1) . (p3 - p1) == (220 + 
                  100)^2, (p3 - p4) . (p3 - p4) == 
            160^2}, {x, 250}, {y, 160}]
φmax = 180 - 
          ArcTan[y/(x - 250)]/
            Degree /. p3max

p3min = 
      FindRoot[{(p3 - p1) . (p3 - p1) == (220 - 
                  100)^2, (p3 - p4) . (p3 - p4) == 
            160^2}, {x, 250}, {y, 160}]
φmin = 
      ArcTan[y/(250 - x)]/Degree   /. p3min

p3f := {x, y} /. 
        FindRoot[{(p3 - p2) . (p3 - p2) == 
              220^2, (p3 - p4) . (p3 - p4) == 160^2}, {x, 
            250}, {y, 160}]
zuall = 
      Table[
ListPlot[{p1, p2, p3f, p4}, 
          PlotJoined ->  True, 
          PlotRange -> {{-100, 350}, {-100, 200}}, 
          PlotStyle ->  Hue[0.9]], {θ, 60  °, 
          390  °, 30  °}]

zu100 = Graphics[Circle[{0, 0}, 100]]
zu160 = Graphics[Circle[{250, 0}, 160]]

Show[zuall, zu100, zu160]