Question 1039936: Need help drawing two right triangles ΔABC and ΔDEF for which sin A = sin D. What can you conclude about ΔABC and ΔDEF?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Since you don't specify which of the vertices of ABC or DEF is the right angle, then you cannot come to any particular conclusion about the two triangles.
Since they are right triangles, you know that one of the angles measures 90 degrees and the other two angles are acute. If you had specified that angle A and angle D were acute angles and not the right angle of the triangle, then you could say that since the sines of the two angles are equal, the measures of the two angles must be equal and since the two right angles have equal measure, the third angle of the triangles must also be congruent. Therefore, the two right angles are similar.
However, the way you posed the problem, angles A and D could be the right angles. So the fact that their sines are equal doesn't say anything at all about the other two angles.
John
My calculator said it, I believe it, that settles it
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