A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 89m long and 70m wide.
1 answer:
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First of all, this problem is properly done with the Law of Cosines, which tells us
giving us a quadratic equation for b we can solve. But let's do it with the Law of Sines as asked.
We have c,a,A so the Law of Sines gives us sin C
There are two possible triangle angles with this sine, supplementary angles, one acute, one obtuse:
Both of these make a valid triangle with A=20°. They give respective B's:
So we get two possibilities for b:
Answer: 2.3 units and 7.8 units
Let's check it with the Law of Cosines:
There's a shortcut for the quadratic formula when the middle term is 'even.'
Looks good.