How to know if the tringal is congruent
2 answers:
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Answer:
a) 9
b)
c) 15
Step-by-step explanation:
The first step is to cancel out the fraction's denominator if possible.
a)
We can cancel the 5 out since 15 divided by 5 is 3. The answer that comes out is
Since 3/1 is 3, we can now simplify the values:
b)
4 is indivisible by three and gives a non-whole value. This is not what we need here.
Instead we should do the division rule and find the remainder.
In this case, 4 divided by 3 gives 1 with a remainder of 1.
After we simplify the non-mixed fraction, we have to change it into a mixed fraction, which consists of a whole number and a fraction. We can split it into the following:
The r1 is just the remainder of the fraction. Since we cannot remove 1 from the remainder, we add it back into the fraction's denominator of 3. This gives:
c)
For this part, we can cancel out 2 since 6 is divisible by 2. This gives:
Since 5/1 is 5,
we can now solve part c:
Double angle identity for cosine:
By the Pythagorean theorem, if
, it follows that 
:
where we take the positive root because
, and 
is non-negative throughout this domain.
So we have
By the Pythagorean theorem, if
where we take the positive root because
So we have