Calculate side DC in this triangle

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    Dc Triangle
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The discussion focuses on calculating the length of side DC in a triangle with given dimensions AD=48cm and BD=17cm. Participants confirm that the calculations appear correct and suggest using the sine and cosine formulas for verification. Additionally, they recommend checking the result by using BC, BD, and the 42° angle. Overall, the calculations are validated, and the approach is deemed appropriate.
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Homework Statement
AD=48cm
BD=17cm
Calculate DC
Relevant Equations
Sine formula and cosine formula
1587315528457.png

Was just wondering if someone could take a look at my calculations and see if I've done them correctly.
1587319123492.png
 
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VitaminK said:
Homework Statement:: AD=48cm
BD=17cm
Calculate DC
Relevant Equations:: Sine formula and cosine formula

View attachment 260979
Was just wondering if someone could take a look at my calculations and see if I've done them correctly.
View attachment 260981
That looks fine.

Of course, you could have found length DC using BC, BD, and angle C (the 42° angle). Maybe, use this as a check.
 
SammyS said:
That looks fine.

Of course, you could have found length DC using BC, BD, and angle C (the 42° angle). Maybe, use this as a check.
thanks!
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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