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Special Right Triangles: 45-45-90 and 30-60-90

11 Questions

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Special Right Triangles: 45-45-90 and 30-60-90

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Questions and Answers

What is the ratio of the hypotenuse to the length of the leg in a 45-45-90 triangle?

1:2

2:1

1:1

√2:1 (correct)

In a 30-60-90 triangle, what is the ratio of the longer leg to the shorter leg?

1:3

2:1

3:1 (correct)

1:2

How can you find the value of the leg in a 45-45-90 triangle?

Divide the hypotenuse by √2 (correct)

Divide the hypotenuse by 2

Multiply the hypotenuse by 2

Multiply the hypotenuse by √2

What is the identifying feature of the hypotenuse in a right triangle?

It is directly across from the 90° angle Signup and view all the answers

How can you find the value of the hypotenuse in a 45-45-90 triangle?

Multiply the leg by √2 Signup and view all the answers

What is the angle opposite to the shorter leg in a 30-60-90 triangle?

30° Signup and view all the answers

How do you find the length of the hypotenuse in a 30-60-90 triangle?

Multiply the shorter leg by 2 Signup and view all the answers

What is the ratio of the longer leg to the shorter leg in a 30-60-90 triangle?

3:2 Signup and view all the answers

If you know the length of the hypotenuse, how do you find the length of the shorter leg?

Divide the hypotenuse by 2 Signup and view all the answers

What is the advantage of finding the shorter leg first in a 30-60-90 triangle?

It makes the calculation easier Signup and view all the answers

If you know the length of the longer leg, how do you find the length of the shorter leg?

Divide the longer leg by 3 Signup and view all the answers

Study Notes

30-60-90 Triangle

The shorter leg is opposite the 30° angle, and the longer leg is opposite the 60° angle.
To find the hypotenuse, multiply the shorter leg by 2.
To find the longer leg, multiply the shorter leg by √3.
To find the shorter leg (given the hypotenuse), divide the hypotenuse by 2.
To find the shorter leg (given the longer leg), divide the longer leg by √3.

45-45-90 Triangle

The hypotenuse is √2 times the length of the leg.
To find the hypotenuse, multiply the leg by √2.
To find the leg, divide the hypotenuse by √2.

Key Facts

In a right triangle, the hypotenuse is always opposite the 90° angle.
Identifying the shorter and longer legs in a 30-60-90 triangle is crucial for solving problems.
Finding the shorter leg first can make it easier to solve problems in a 30-60-90 triangle.

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Description

Test your understanding of special right triangles, including 45-45-90 and 30-60-90 triangles, with exercises on finding the hypotenuse and leg lengths. Practice solving problems and apply mathematical formulas to find the values of x, a, and b.