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

In summary, a high school student is seeking help in finding the length of DC in a 30-60-90 triangle with a height of 6. They are unsure of how to proceed due to the lack of information and varying lengths of BC. However, it is mentioned that more information, such as AD = AC, would be needed to solve the problem.
  • #1
Dophs
1
0
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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  • #2
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
 
  • #3
Thanks for reply and it is very informative.
 

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

What is a right triangle?

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees. This angle is known as the right angle and is formed by the intersection of the two shorter sides of the triangle.

What is the Pythagorean Theorem?

The Pythagorean Theorem is a mathematical equation that relates the lengths of the three sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

How do you find the length of the sides of a right triangle?

The length of the sides of a right triangle can be found using the Pythagorean Theorem or by using trigonometric functions such as sine, cosine, and tangent. The length of the hypotenuse can also be found using the square root of the sum of the squares of the other two sides.

What is the relationship between the sides of a right triangle?

In a right triangle, the length of the hypotenuse is always the longest side, while the other two sides are known as the legs. The Pythagorean Theorem and trigonometric functions can be used to find the exact relationship between the lengths of the sides.

Can a right triangle have two sides of the same length?

Yes, a right triangle can have two sides of the same length. This type of right triangle is called an isosceles right triangle and has two equal legs. The length of the hypotenuse can be found by using the Pythagorean Theorem.

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