Analyze the given parts, state of the given information would create a unique triangle, multiple triangles, or no triangle.
It has a right angle which label as J and there is two acute angles label as K and L
A. this information resulted in a unique triangle
B. This information could resulted in many different triangles
C. This information resulted in no triangles
My answer is B can someone check if it right?
the size of the angles is given ... but the length of the sides is not
an infinite number of similar triangles can be made
... by varying the side lengths
I hate to burst your bubble, but your answer is wrong. The correct answer is A, this information resulted in a unique triangle. You see, in a right triangle, one angle will always be 90 degrees, which is labeled as J in this case. The other two angles are acute angles, labeled as K and L. Therefore, there can only be one combination of these angles that satisfy the conditions of a right triangle. So, no multiple triangles or no triangle at all. Just one unique triangle. Keep calm and math on!
Your answer is correct. The given information of a right angle (labelled as J) and two acute angles (labelled as K and L) can result in many different triangles. In a right triangle, the sum of the two acute angles is always 90 degrees. However, there can be multiple combinations of acute angles that satisfy this condition. Therefore, the information given does not specifically determine a unique triangle, making option B the correct choice.
To determine whether the given information results in a unique triangle, multiple triangles, or no triangle, we need to use the rules and properties of triangles.
In a triangle, the sum of all interior angles is always 180 degrees.
Given that one angle is labeled as a right angle (J), which measures 90 degrees, and the other two angles are labeled as acute angles (K and L), we know that both K and L are less than 90 degrees.
Now, if we assume that both K and L are greater than 0 degrees, the sum of the three angles in the triangle would be 90 + K + L, which must be equal to 180 degrees.
However, there are infinite values of K and L that satisfy the condition K + L = 90 degrees, which means there are multiple possible values for triangles. For example, if K = 30 degrees, L = 60 degrees, the triangle would have a right angle of 90 degrees.
Therefore, the correct answer is B. This information could result in many different triangles.