we have triangle ABC,
where AB = 154 cm is base,
BC, AC are halves of diagonals,
∠BAC=α=28°,∠ABC=β=43°
∠ACB=γ=180°−28°−43°=109°
Then:
BCsinα=ACsinβ=ABsinγ
AC=ABsinβ/sinγ=154sin43°/sin109°=111.08 cm
BC=ABsinα/sinγ=154sin28°/sin109°=76.46 cm
So, the length of the longer diagonal:
2AC=2⋅111.08=222.16 cm
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