507,990 views
23 votes
23 votes
I need help finding the vortex angle with these three sides. I don’t really know how to do this sort of thing with an isosceles triangle. Once I know the vortex angle I can figure out the base angles.

I need help finding the vortex angle with these three sides. I don’t really know how-example-1
User Seorphates
by
3.1k points

1 Answer

21 votes
21 votes

Answer:


\begin{gathered} \text{ Smalles angle in the triangle}\colon \\ D=14.36\degree \\ \text{ The measure of the two congruent angles:} \\ <strong>Step-by-step explanation:</strong><p>To find the angle D, use the law of cosines, which is represented as:</p>[tex]\begin{gathered} d^2=e^2+f^2-2(e)(f)\cos D \\ 3^2=12^2+12^2-2(12)(12)\cos D \\ 9=144+144-288\cos D \\ -279==-288\cos D \\ (-279)/(-288)=\cos D \\ D=\cos ^(-1)((-279)/(-288)) \\ D=14.36\degree \end{gathered}

Then, since the base angles are equal in measure:

[tex]\begin{gathered}
User Sahil Gupta
by
2.6k points