11 Questions
What is the ratio of the hypotenuse to the length of the leg in a 45-45-90 triangle?
√2:1
In a 30-60-90 triangle, what is the ratio of the longer leg to the shorter leg?
3:1
How can you find the value of the leg in a 45-45-90 triangle?
Divide the hypotenuse by √2
What is the identifying feature of the hypotenuse in a right triangle?
It is directly across from the 90° angle
How can you find the value of the hypotenuse in a 45-45-90 triangle?
Multiply the leg by √2
What is the angle opposite to the shorter leg in a 30-60-90 triangle?
30°
How do you find the length of the hypotenuse in a 30-60-90 triangle?
Multiply the shorter leg by 2
What is the ratio of the longer leg to the shorter leg in a 30-60-90 triangle?
3:2
If you know the length of the hypotenuse, how do you find the length of the shorter leg?
Divide the hypotenuse by 2
What is the advantage of finding the shorter leg first in a 30-60-90 triangle?
It makes the calculation easier
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
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.
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.
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