The Hypotenuse Of A $45^{\circ}-45^{\circ}-90^{\circ}$ Triangle Measures $7 \sqrt{2}$ Units.What Is The Length Of One Leg Of The Triangle?A. 7 Units B. \$7 \sqrt{2}$[/tex\] Units C. 14 Units D. $14
Introduction
In the realm of geometry, triangles are fundamental shapes that have been studied extensively. One of the most common types of triangles is the 45°-45°-90° triangle, also known as the isosceles right triangle. This triangle has two equal legs and a hypotenuse that is √2 times the length of each leg. In this article, we will explore the relationship between the hypotenuse and the legs of a 45°-45°-90° triangle, and use this knowledge to solve a problem involving the length of one leg.
The Relationship Between the Hypotenuse and the Legs of a 45°-45°-90° Triangle
A 45°-45°-90° triangle is a special type of right triangle where the two legs are equal in length, and the hypotenuse is √2 times the length of each leg. This relationship can be expressed mathematically as:
c = a√2
where c is the length of the hypotenuse, and a is the length of each leg.
Understanding the Problem
The problem states that the hypotenuse of a 45°-45°-90° triangle measures 7√2 units. We are asked to find the length of one leg of the triangle. To solve this problem, we can use the relationship between the hypotenuse and the legs of a 45°-45°-90° triangle.
Solving the Problem
Using the relationship c = a√2, we can substitute the given value of the hypotenuse (7√2) into the equation:
7√2 = a√2
To solve for a, we can divide both sides of the equation by √2:
a = 7√2 / √2
Simplifying the equation, we get:
a = 7
Therefore, the length of one leg of the triangle is 7 units.
Conclusion
In this article, we explored the relationship between the hypotenuse and the legs of a 45°-45°-90° triangle. We used this knowledge to solve a problem involving the length of one leg of a triangle with a hypotenuse of 7√2 units. The solution to the problem is a = 7 units, which is option A.
Frequently Asked Questions
- What is the relationship between the hypotenuse and the legs of a 45°-45°-90° triangle? The relationship between the hypotenuse and the legs of a 45°-45°-90° triangle is c = a√2, where c is the length of the hypotenuse, and a is the length of each leg.
- How do you find the length of one leg of a 45°-45°-90° triangle? To find the length of one leg of a 45°-45°-90° triangle, you can use the relationship c = a√2, and substitute the given value of the hypotenuse into the equation.
- What is the length of one leg of a 45°-45°-90° triangle with a hypotenuse of 7√2 units? The length of one leg of a 45°-45°-90° triangle with a hypotenuse of 7√2 units is 7 units.
Key Takeaways
- The relationship between the hypotenuse and the legs of a 45°-45°-90° triangle is c = a√2.
- To find the length of one leg of a 45°-45°-90° triangle, you can use the relationship c = a√2, and substitute the given value of the hypotenuse into the equation.
- The length of one leg of a 45°-45°-90° triangle with a hypotenuse of 7√2 units is 7 units.
Introduction
In our previous article, we explored the relationship between the hypotenuse and the legs of a 45°-45°-90° triangle. We used this knowledge to solve a problem involving the length of one leg of a triangle with a hypotenuse of 7√2 units. In this article, we will answer some frequently asked questions about the hypotenuse of a 45°-45°-90° triangle.
Q&A
Q: What is the relationship between the hypotenuse and the legs of a 45°-45°-90° triangle?
A: The relationship between the hypotenuse and the legs of a 45°-45°-90° triangle is c = a√2, where c is the length of the hypotenuse, and a is the length of each leg.
Q: How do you find the length of one leg of a 45°-45°-90° triangle?
A: To find the length of one leg of a 45°-45°-90° triangle, you can use the relationship c = a√2, and substitute the given value of the hypotenuse into the equation.
Q: What is the length of one leg of a 45°-45°-90° triangle with a hypotenuse of 7√2 units?
A: The length of one leg of a 45°-45°-90° triangle with a hypotenuse of 7√2 units is 7 units.
Q: Can you explain why the hypotenuse of a 45°-45°-90° triangle is √2 times the length of each leg?
A: The hypotenuse of a 45°-45°-90° triangle is √2 times the length of each leg because the triangle is formed by two 45° angles and a 90° angle. The two 45° angles create a right triangle with a hypotenuse that is √2 times the length of each leg.
Q: How do you know that the triangle is a 45°-45°-90° triangle?
A: You can determine that the triangle is a 45°-45°-90° triangle by looking at the angles. If the triangle has two 45° angles and a 90° angle, it is a 45°-45°-90° triangle.
Q: Can you give an example of a 45°-45°-90° triangle?
A: A classic example of a 45°-45°-90° triangle is a square with a diagonal. The diagonal of the square is the hypotenuse of the triangle, and the sides of the square are the legs of the triangle.
Q: How do you use the relationship c = a√2 to solve problems involving the hypotenuse of a 45°-45°-90° triangle?
A: To use the relationship c = a√2 to solve problems involving the hypotenuse of a 45°-45°-90° triangle, you can substitute the given value of the hypotenuse into the equation and solve for the length of each leg.
Conclusion
In this article, we answered some frequently asked questions about the hypotenuse of a 45°-45°-90° triangle. We covered topics such as the relationship between the hypotenuse and the legs of a 45°-45°-90° triangle, how to find the length of one leg of a 45°-45°-90° triangle, and how to use the relationship c = a√2 to solve problems involving the hypotenuse of a 45°-45°-90° triangle.
Frequently Asked Questions
- What is the relationship between the hypotenuse and the legs of a 45°-45°-90° triangle? The relationship between the hypotenuse and the legs of a 45°-45°-90° triangle is c = a√2, where c is the length of the hypotenuse, and a is the length of each leg.
- How do you find the length of one leg of a 45°-45°-90° triangle? To find the length of one leg of a 45°-45°-90° triangle, you can use the relationship c = a√2, and substitute the given value of the hypotenuse into the equation.
- What is the length of one leg of a 45°-45°-90° triangle with a hypotenuse of 7√2 units? The length of one leg of a 45°-45°-90° triangle with a hypotenuse of 7√2 units is 7 units.
Key Takeaways
- The relationship between the hypotenuse and the legs of a 45°-45°-90° triangle is c = a√2.
- To find the length of one leg of a 45°-45°-90° triangle, you can use the relationship c = a√2, and substitute the given value of the hypotenuse into the equation.
- The length of one leg of a 45°-45°-90° triangle with a hypotenuse of 7√2 units is 7 units.