Math Problem Statement
Solution
The triangle in the image is a 45°-45°-90° triangle, which is a special right triangle. In this type of triangle, the two legs are equal in length, and the relationship between the legs and the hypotenuse follows the ratio .
From the image:
- The hypotenuse is given as .
To find the length of the leg , we can use the following formula for 45°-45°-90° triangles:
Given that the hypotenuse is , we substitute this into the formula:
Now, solve for :
So, the length of leg is .
The correct answer is D. 3.
Would you like more details or have any further questions?
Here are 5 related questions you might find interesting:
- How is the ratio derived for a 45°-45°-90° triangle?
- Can the Pythagorean theorem be used to verify the result for a 45°-45°-90° triangle?
- How do special right triangles differ from general right triangles?
- What are the properties of other special triangles, such as 30°-60°-90° triangles?
- How can you generalize the formula for finding the legs of a right triangle given different angles?
Tip: In 45°-45°-90° triangles, knowing one leg allows you to find both the other leg and the hypotenuse easily using simple ratios!
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Math Problem Analysis
Mathematical Concepts
Geometry
Special Right Triangles
Formulas
Hypotenuse = s * sqrt(2)
Theorems
45°-45°-90° triangle theorem
Suitable Grade Level
Grades 8-10