Question

Given the triangle with angles of \( 40^\circ \), \( 50^\circ \), and \( 90^\circ \), compare the legs of this triangle to those of a \( 45^\circ \)-\( 45^\circ \)-\( 90^\circ \) triangle. 

• A. Quantity A is greater
• B. Quantity B is greater
• C. The two quantities are equal
• D. The relationship cannot be determined from the information given.
• E.

Hint:

To compare triangles, always ensure you have sufficient information, such as side lengths or additional properties.

Answer 1

The Correct Option is D

Step 1: Understand the angles.
The question provides a triangle with angles \( 40^\circ \), \( 50^\circ \), and \( 90^\circ \). We are asked to compare its legs with those of a \( 45^\circ \)-\( 45^\circ \)-\( 90^\circ \) triangle.
Step 2: Consider the relationship between the two triangles.
For the \( 45^\circ \)-\( 45^\circ \)-\( 90^\circ \) triangle, the legs are equal, but we don’t have enough information about the triangle in the question to establish a clear relationship.
Step 3: Conclusion.
Without knowing the lengths of the sides or any other properties, the relationship cannot be determined.
Final Answer: \[ \boxed{\text{The correct answer is (4) The relationship cannot be determined from the information given.}} \]