I climb half the steps in a staircase. Next, I climb one-third of the remaining steps. Then I climb one-eight of the rest and st
1 answer:
Given parameters:
First sets of staircase =
Next sets =
Third sets =
Unknown:
The least possible number of steps =?
Solution:
The least possible number of steps will be the lowest common multiples of these sets of steps.
We want fractions that will give whole numbers because realistically, one cannot take half a step of a step.
So, the number of steps must be a multiple of denominators of the fractions given.
Denominators are 2 , 3 and 8
Their least common multiple is 24;
This the lowest number by which 2, 3 and 8 can all divide.
So, the least number is 24 steps
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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.