Question

solve the triangles

Answer 1

Where is the triangle ? O.o

Answer 2

Hi :) It's quite simple, really. I think we can use trigonometry to solve this question. Since sin 15 degrees is 4 over the number you want to find, simply punch that into the calculator, and you will get your number :)

Note that sin of an angle is equal to opposite over hypotenuse side. So sin(15) * 4 = your answer :)

Hope that helped, have a nice day! :)

Answer 3

Let A, B and C be the vertex of the triangle where :
\[A=15^\circ\\
b=AC=3\\
c=AB=4
\]
Fist, we calculate a=BC.
From the Cosine low we have :
\[\cos A=\frac{b^2+c^2-a^2}{2bc}\]
So :
\[a^2=b^2+c^2-2bc\cos A=9+16-24\cos15^\circ\simeq1.8178\]
So :
\[a=\sqrt{1.8178}=1.348\]
Now, by the Sines' Low we can find the other angles :
\[\frac{\sin B}{b}=\frac{\sin A}{a}\Rightarrow \sin B=\frac{b\sin A}{a}=\frac{3\times\sin15^\circ}{1.348}\simeq0.576\]
And then :
\[B=\sin^{-1}(0.576)=35.16^\circ\]
Now :
\[C=180^\circ-A-B=180^\circ-15^\circ-35.16^\circ=129.84^\circ\]

Answer 4

@RaineJones that formula only works if one of the angles in the triangle is 90 degrees, otherwise you have to resort to the Law of Sines

Answer 5

@jack1 thanks for pointing that out! :)