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One corner of a triangle has a 60° angle and the length of the two adjacent sides are in ratio 1 : 3.
Calculate the angles of the other triangle corners (0,1°:s precision, 1 point / correct angle).
 3 years ago
 3 years ago
One corner of a triangle has a 60° angle and the length of the two adjacent sides are in ratio 1 : 3. Calculate the angles of the other triangle corners (0,1°:s precision, 1 point / correct angle).
 3 years ago
 3 years ago

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BecomeMyFan=DBest ResponseYou've already chosen the best response.0
I think I have to first find the size of the opposite side to 60 degree angle right? i used cosine rule to do so and found 2.65, however I dont know what to do now
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Yes, you're on the right track. Now use sine rule to find your angles...but, note you only have to use it once because the sum of the angles of a plane triangle is 180 degrees (and by the time you apply the sine rule, you'll have two of them).
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
ok, so then I just sub the 2 angs form 180 and.... right?
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
First find one of the other angles.
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
something is not right
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
I think you found the sum of 60 and one of the other ones, 19.1.
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
is 2.645 right for the third side?
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
\[\frac{a}{\sin \theta}=\frac{\sqrt{7} a}{\sin 60^o}\]
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
i found one angle to be 19.1
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Your third side is right, assuming, in your ratio of 1:3, the side with the '1' has unit length. A more general assumption is that this side has length 'a', so that the other side has length 3a.
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
The side opposite 60 degrees would then have length,\[\sqrt{7}a\]
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
oh, yeah, i get it
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
How? Cosine rule, like you used before (if you're asking how I get sqrt(7)a?).
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Once the other angle's found, you're done.
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
ok, subing 19.1+60 from 180 gives 100.9
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
when i try to find the last angle using sine rule, it gives me 79.2
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
i did something wrong then
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
In mathematics, if you end up with a contradiction, it's because one of your assumptions is wrong...so what assumption(s) were made?
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
the ratio of sides 1 to 3, the sine rule, the cosine rule and the 60 angle
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Does your question say "the length of *the* two adjacent sides" or "the length of two adjacent sides"?
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
whats the difference?
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
'the' restricts your choice
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
but i still dont see what I did wrong :(
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Omg, it just dawned on me  there are two possible solutions!
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
One set will have (60, 9.1 and the other) and (60, 79.2, other)
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
One assumption was missed  that there is only one solution.
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
I constructed a triangle on the description in GeoGebra and have (60,9.1,100.9) as one solution.
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
:) so there is just one solution?
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
No, it's coming about because the arc of sine (in on rotation) has TWO angles whose sine is positive and the same value.
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
so, is it then imposible to find both of the angles correctly?
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
No, it's just that you collect both possible solutions from the arc of sine on each angle, and then put them in the appropriate combinations (i.e. so they add to 180).
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
so, how do I answer the quesstion in a work book? which set of angles do I choose?
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
ok..I'm trying to figure out a way to do it so that it doesn't take a millennium to type.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
wouldn't the other angle be 30 and the other 90?
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
since the other is 60?
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
\[\frac{\sin \alpha}{3a}=\frac{\sin 60}{\sqrt{7}a}\rightarrow \sin \alpha = \frac{3\sqrt{3}}{2\sqrt{7}}\]
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
in the arc of 360 degrees, \[\alpha = \sin^{1}\frac{3\sqrt{3}}{2\sqrt{7}}\] degrees AND\[\alpha = 180 \sin^{1}\frac{3\sqrt{3}}{2\sqrt{7}}\]
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
where \[\sin^{1}\frac{3\sqrt{3}}{2\sqrt{7}}\approx 79.1^o\]
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
So the possible angles you get as solutions when considering this combination of sides is\[79.1^o, 100.9^o\]
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Try taking the sine of both of them in your calculator.
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
So you have NO CHOICE but to accept two solutions for this first combination of sides.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
just one question, is it a right triangle? ^_^
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
the question does not specify
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
because if so, then the other 2 angles are 90 and 30, otherwise , loki's answer is true :)
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
When you take the arc of sine here you'll get two solutions for each angle, which are algebraically correct.
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
So, calling those angles alpha and beta, you have\[\alpha \in \left\{ 79.1,100.9 \right\}\]and\[\beta \in \left\{ 19.1, 160.9 \right\}\]
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
only certain combinations of those angles will give you a true conclusion here, since you have an additional constraint: that the angles\[\alpha, \beta, 60^o\]must sum to 180 degrees.
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
So you have to find those combinations elements from the set of alpha and beta that will allow you to get 180 (after you add 60 to them). You see?
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
then alpha is 100.9 and beta is 19.1 ?
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
There are four possible combinations, but only ONE combination works
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
and he strikes again~ lol
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
and i;m drunk  came back from a dinner
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
but you've answered it , weirdly in such a state ._. did you get it andy?
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
It's similar to a situation when you have to solve the quadratic equation, which might have something to do with length, and you get two solutions  one positive, one negative. You apply an additional constraint (i.e. physical measurements aren't negative) and discard one of the solutions. Here, the constraint is that you can only take those angles whose sum will be 180.
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
and, lokisan, you dont sound like drunk
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
\[\left\{ \alpha, \beta\alpha + \beta +60^o=180^o , \alpha \in \left\{ 79.1,100.9 \right\},\beta \in \left\{ 19.1,160.9 \right\} \right\}\]
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
discrete mathematics ^^" ...
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
yes...so the above set is 19.1 and 100.9.
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
yeah, it is hard, but i am damn happy
 3 years ago
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