A Right Triangle Has Legs Measuring 20 In. And 28 In. What Is The Length Of The Hypotenuse? Round To The Nearest Tenth.A. 8.0 In. B. 19.6 In. C. 34.4 In. D. 1184.0 In.
Introduction
In this article, we will explore the concept of right triangles and how to find the length of the hypotenuse using the Pythagorean theorem. A right triangle is a triangle with one angle that is 90 degrees. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The Pythagorean Theorem
The Pythagorean theorem is a fundamental concept in geometry and is used to find the length of the hypotenuse of a right triangle. The theorem is stated as:
a^2 + b^2 = c^2
where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse.
Applying the Pythagorean Theorem to the Problem
In this problem, we are given the lengths of the legs of the right triangle as 20 inches and 28 inches. We need to find the length of the hypotenuse. Using the Pythagorean theorem, we can plug in the values as follows:
a = 20 inches b = 28 inches c = ?
Substituting the values into the equation, we get:
20^2 + 28^2 = c^2 400 + 784 = c^2 1184 = c^2
Finding the Length of the Hypotenuse
To find the length of the hypotenuse, we need to take the square root of both sides of the equation:
c = √1184 c ≈ 34.4 inches
Therefore, the length of the hypotenuse is approximately 34.4 inches.
Conclusion
In this article, we used the Pythagorean theorem to find the length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches. We applied the theorem by plugging in the values and solving for the length of the hypotenuse. The result was approximately 34.4 inches.
Why the Other Options are Incorrect
Let's take a look at the other options:
A. 8.0 in. - This is clearly incorrect, as the length of the hypotenuse cannot be less than the length of the legs.
B. 19.6 in. - This is also incorrect, as the length of the hypotenuse is greater than the length of the legs.
D. 1184.0 in. - This is incorrect, as the length of the hypotenuse is the square root of 1184, not 1184 itself.
Real-World Applications of the Pythagorean Theorem
The Pythagorean theorem has many real-world applications, including:
- Building design: Architects use the Pythagorean theorem to design buildings and ensure that the walls and floors are perpendicular.
- Surveying: Surveyors use the Pythagorean theorem to measure distances and angles in the field.
- Physics: Physicists use the Pythagorean theorem to calculate distances and velocities in problems involving right triangles.
Conclusion
Q&A: Frequently Asked Questions about Right Triangles and the Pythagorean Theorem
Q: What is a right triangle?
A: A right triangle is a triangle with one angle that is 90 degrees. The side opposite the right angle is called the hypotenuse.
Q: What is the Pythagorean theorem?
A: The Pythagorean theorem is a mathematical formula that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The formula is:
a^2 + b^2 = c^2
where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse.
Q: How do I use the Pythagorean theorem to find the length of the hypotenuse?
A: To use the Pythagorean theorem to find the length of the hypotenuse, you need to know the lengths of the two legs of the right triangle. You can then plug these values into the formula and solve for the length of the hypotenuse.
Q: What if I don't know the lengths of the legs of the right triangle?
A: If you don't know the lengths of the legs of the right triangle, you can use other methods to find the length of the hypotenuse. For example, you can use trigonometry or other geometric formulas to find the length of the hypotenuse.
Q: Can I use the Pythagorean theorem to find the length of the legs of the right triangle?
A: Yes, you can use the Pythagorean theorem to find the length of the legs of the right triangle. If you know the length of the hypotenuse and one of the legs, you can use the formula to find the length of the other leg.
Q: What are some real-world applications of the Pythagorean theorem?
A: The Pythagorean theorem has many real-world applications, including:
- Building design: Architects use the Pythagorean theorem to design buildings and ensure that the walls and floors are perpendicular.
- Surveying: Surveyors use the Pythagorean theorem to measure distances and angles in the field.
- Physics: Physicists use the Pythagorean theorem to calculate distances and velocities in problems involving right triangles.
Q: Can I use the Pythagorean theorem to find the area of a right triangle?
A: Yes, you can use the Pythagorean theorem to find the area of a right triangle. The area of a right triangle is equal to half the product of the lengths of the legs. You can use the formula:
Area = (1/2)ab
where a and b are the lengths of the legs of the right triangle.
Q: Can I use the Pythagorean theorem to find the perimeter of a right triangle?
A: Yes, you can use the Pythagorean theorem to find the perimeter of a right triangle. The perimeter of a right triangle is equal to the sum of the lengths of the three sides. You can use the formula:
Perimeter = a + b + c
where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse.
Conclusion
In conclusion, the Pythagorean theorem is a powerful tool for finding the length of the hypotenuse of a right triangle. By understanding the theorem and how to apply it, you can solve a wide range of problems involving right triangles. Whether you're a student, a professional, or just someone who loves math, the Pythagorean theorem is an essential tool to have in your toolkit.