Triangles (45/45/90) - Hypotenuse to Short Side

Level 1

This math topic focuses on solving problems related to 45/45/90 triangles, specifically finding the relationship between the hypotenuse and the short sides using principles of Pythagorean theorem. It enhances students’ understanding of right triangles, trigonometric ratios, and square root operations. Each problem includes a diagram of a triangle and requires calculation to find a missing length, either by deriving it as a multiple or fraction of known dimensions. Given answers are expressed in simplified radical forms, further practicing algebraic simplification and manipulation skills.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Triangles (45/45/90) - Hypotenuse to Short Side Worksheet

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Triangles (45/45/90) - Hypotenuse to Short Side
1
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing 2square root of 3
b A LaTex expression showing 2square root of 2
2
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing 3
b A LaTex expression showing 3square root of 2
3
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing \frac{square root of 3}{2}
b A LaTex expression showing \frac{square root of 2}{2}
4
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing square root of 2
b A LaTex expression showing 2
5
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing 1
b A LaTex expression showing \frac{square root of 2}{2}
6
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing \frac{7square root of 3}{2}
b A LaTex expression showing \frac{7square root of 2}{2}
7
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing \frac{3square root of 2}{2}
b A LaTex expression showing 3
8
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing 3square root of 3
b A LaTex expression showing 3square root of 2