Triangles (30/60/90) - Medium Side to Hypotenuse

Level 1

This math topic focuses on finding missing side lengths of 30-60-90 triangles using the relationships between the sides derived from the Pythagorean theorem. The problems require students to apply knowledge of specific triangle side ratios (1:√3:2) to solve for either the medium side or the hypotenuse when only one side length is given. This practice is nested within a broader study of Pythagoras’ theorem, enhancing understanding of right-angle triangle properties. Each question involves problem-solving where students utilize algebraic manipulation and familiar geometric principles to find the desired length.

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

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Triangles (30/60/90) - Medium Side to Hypotenuse Worksheet

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Triangles (30/60/90) - Medium Side to Hypotenuse
1
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 2
2
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing 5 over 2
b A LaTex expression showing 5
3
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing 7
b A LaTex expression showing 7 over 2
4
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 6
5
An svg image showing a math problem
Solve for the missing length on this triangle
a A LaTex expression showing 2
b A LaTex expression showing square root of 3
6
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 2
7
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 1 over 2
8
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 1