Calculating the Ratio of the Length of One Leg to the Length of the Other Leg

Oct 13, 2025 by windailys.com 58 views

A 45-45-90 right 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. In this article, we will explore the properties of a 45-45-90 right triangle and determine the ratio of the length of one leg to the length of the other leg.

What is a 45-45-90 Right Triangle?

A 45-45-90 right triangle is a right triangle with two angles that measure 45 degrees each. The third angle, which is the right angle, measures 90 degrees. This type of triangle is also known as an isosceles right triangle because the two legs are equal in length.

Properties of a 45-45-90 Right Triangle

The properties of a 45-45-90 right triangle are as follows:

The two legs are equal in length.
The hypotenuse is √2 times the length of each leg.
The angles are 45-45-90 degrees.

Calculating the Ratio of the Length of One Leg to the Length of the Other Leg

To calculate the ratio of the length of one leg to the length of the other leg, we can use the properties of a 45-45-90 right triangle. Since the two legs are equal in length, the ratio of the length of one leg to the length of the other leg is 1:1.

Why is the Ratio 1:1?

The ratio of the length of one leg to the length of the other leg is 1:1 because the two legs are equal in length. This means that if one leg is 5 units long, the other leg is also 5 units long. Therefore, the ratio of the length of one leg to the length of the other leg is 5:5 or 1:1.

Conclusion

In conclusion, the ratio of the length of one leg to the length of the other leg in a 45-45-90 right triangle is 1:1. This is because the two legs are equal in length, and the hypotenuse is √2 times the length of each leg.

Answer

The correct answer is C. 1:1.

Additional Information

Here are some additional facts about 45-45-90 right triangles:

The Pythagorean theorem states that a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse.
The hypotenuse of a 45-45-90 right triangle is √2 times the length of each leg.
The angles of a 45-45-90 right triangle are 45-45-90 degrees.

Real-World Applications

45-45-90 right triangles have many real-world applications, including:

Building design: 45-45-90 right triangles are often used in building design to create symmetrical and aesthetically pleasing structures.
Engineering: 45-45-90 right triangles are used in engineering to calculate stresses and strains on structures.
Physics: 45-45-90 right triangles are used in physics to calculate distances and velocities.

Conclusion

Q: What is a 45-45-90 right triangle?

A: A 45-45-90 right 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.

Q: What are the properties of a 45-45-90 right triangle?

A: The properties of a 45-45-90 right triangle are as follows:

The two legs are equal in length.
The hypotenuse is √2 times the length of each leg.
The angles are 45-45-90 degrees.

Q: How do I calculate the length of the hypotenuse of a 45-45-90 right triangle?

A: To calculate the length of the hypotenuse of a 45-45-90 right triangle, you can use the formula: c = √2 * a, where c is the length of the hypotenuse and a is the length of each leg.

Q: How do I calculate the length of one leg of a 45-45-90 right triangle?

A: To calculate the length of one leg of a 45-45-90 right triangle, you can use the formula: a = c / √2, where a is the length of each leg and c is the length of the hypotenuse.

Q: What is the ratio of the length of one leg to the length of the other leg in a 45-45-90 right triangle?

A: The ratio of the length of one leg to the length of the other leg in a 45-45-90 right triangle is 1:1.

Q: What are some real-world applications of 45-45-90 right triangles?

A: 45-45-90 right triangles have many real-world applications, including:

Building design: 45-45-90 right triangles are often used in building design to create symmetrical and aesthetically pleasing structures.
Engineering: 45-45-90 right triangles are used in engineering to calculate stresses and strains on structures.
Physics: 45-45-90 right triangles are used in physics to calculate distances and velocities.

Q: How do I identify a 45-45-90 right triangle?

A: To identify a 45-45-90 right triangle, you can look for the following characteristics:

The two legs are equal in length.
The hypotenuse is √2 times the length of each leg.
The angles are 45-45-90 degrees.

Q: Can I use a 45-45-90 right triangle to solve other types of triangles?

A: Yes, you can use a 45-45-90 right triangle to solve other types of triangles. For example, you can use a 45-45-90 right triangle to calculate the length of the hypotenuse of a 30-60-90 right triangle.

Q: What are some common mistakes to avoid when working with 45-45-90 right triangles?

A: Some common mistakes to avoid when working with 45-45-90 right triangles include:

Assuming that the two legs are not equal in length.
Failing to calculate the length of the hypotenuse correctly.
Not using the correct formula to calculate the length of one leg.

Conclusion

In conclusion, 45-45-90 right triangles are a special type of right triangle with two legs that are equal in length and a hypotenuse that is √2 times the length of each leg. By understanding the properties and applications of 45-45-90 right triangles, you can solve a wide range of problems in mathematics, engineering, and physics.