MHB Length of sides of right triangle with 1 angle and 1 side

AI Thread Summary
The discussion revolves around determining the lengths of the sides of a right triangle given one angle and one side. The triangle in question is a 30-60-90 triangle with a height of 6, but the length of side BC is unspecified, leading to ambiguity in calculations. Participants note that without additional information, such as the relationship between other sides, it is impossible to definitively calculate the lengths. The original poster seeks guidance on whether this question fits within the trigonometry category. The conversation highlights the importance of having sufficient data to solve geometric problems accurately.
Dophs
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Hello so I'm a high school student and I came up with this question and I wanted to know if this was possible to do?

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So I tried to research and find a way to find the length of DC and I couldn't find anything, so I am here to ask for help, is this possible? I figured it would go in the trigonometry section, if not please tell me what sub-forum is belongs in.

So obviously I know the left, right triangle is a 30,60,90 and the height of the right, right triangle is 6 and obviously it has a 90 degree angle. I couldn't think of anyway to get any further due to the not drawn to scale part due to . BC could be 100, 4, 67, 21, so the angles would change of that triangle, but 6 is the height of both.
 

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Dophs said:
Hello so I'm a high school student and I came up with this question and I wanted to know if this was possible to do?
So I tried to research and find a way to find the length of DC and I couldn't find anything, so I am here to ask for help, is this possible? I figured it would go in the trigonometry section, if not please tell me what sub-forum is belongs in.

So obviously I know the left, right triangle is a 30,60,90 and the height of the right, right triangle is 6 and obviously it has a 90 degree angle. I couldn't think of anyway to get any further due to the not drawn to scale part due to . BC could be 100, 4, 67, 21, so the angles would change of that triangle, but 6 is the height of both.
You are right... BC can be any length we like unless we have more information, such as AD = AC.

-Dan
 
Thanks for reply and it is very informative.
 

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