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

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SUMMARY

The discussion centers on determining the lengths of sides in a right triangle, specifically a 30-60-90 triangle, given one angle and one side. The height of the triangle is established as 6 units, but the length of side BC remains undetermined due to the lack of additional information. Participants agree that without further constraints, such as the relationship between sides AD and AC, the length of BC can vary significantly. This highlights the importance of having sufficient data to solve for unknown dimensions in geometric problems.

PREREQUISITES
  • Understanding of 30-60-90 triangle properties
  • Basic trigonometry concepts
  • Knowledge of geometric relationships in triangles
  • Ability to interpret and manipulate algebraic expressions
NEXT STEPS
  • Study the properties of 30-60-90 triangles in detail
  • Learn how to apply the Pythagorean theorem to find unknown sides
  • Explore trigonometric ratios (sine, cosine, tangent) for right triangles
  • Investigate geometric constraints that can determine side lengths
USEFUL FOR

High school students, educators in geometry, and anyone interested in mastering trigonometric principles and solving geometric problems involving right triangles.

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?

View attachment 8044

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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