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 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
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).

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BecomeMyFan=D
 3 years ago
Best ResponseYou've already chosen the best response.0I 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

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0Yes, 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).

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

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

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

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

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

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

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

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0Your 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0No, 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).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0only 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.

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0So 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?

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

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

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

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

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

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0It'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.

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

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

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

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

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