Triangles (30/60/90) With Equilateral Guide - Medium to Short Side

Level 1

This math topic focuses on solving for missing lengths in 30/60/90 triangles using the properties of equilateral triangles, which is a practical application of the Pythagorean theorem. Each problem involves completing an equilateral triangle to find two side lengths of a right triangle using given dimensions and formulas involving square roots. The worksheet is structured with multiple questions, each requiring calculations to derive the side lengths, providing practice in geometry and reinforcing understanding of special right triangles and their relations.

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

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Triangles (30/60/90) With Equilateral Guide - Medium to Short Side Worksheet

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Triangles (30/60/90) With Equilateral Guide - Medium to Short Side
1
An svg image showing a math problem
Solve for the missing length on this triangle by completing the equilateral triangle
a A LaTex expression showing 3
b A LaTex expression showing 3square root of 3
2
An svg image showing a math problem
Solve for the missing length on this triangle by completing the equilateral triangle
a A LaTex expression showing 2
b A LaTex expression showing 4
3
An svg image showing a math problem
Solve for the missing length on this triangle by completing the equilateral triangle
a A LaTex expression showing 5
b A LaTex expression showing 5 over 2
4
An svg image showing a math problem
Solve for the missing length on this triangle by completing the equilateral triangle
a A LaTex expression showing 2
b A LaTex expression showing 2square root of 3
5
An svg image showing a math problem
Solve for the missing length on this triangle by completing the equilateral triangle
a A LaTex expression showing \frac{7square root of 3}{2}
b A LaTex expression showing 7 over 2
6
An svg image showing a math problem
Solve for the missing length on this triangle by completing the equilateral triangle
a A LaTex expression showing 3 over 2
b A LaTex expression showing \frac{3square root of 3}{2}
7
An svg image showing a math problem
Solve for the missing length on this triangle by completing the equilateral triangle
a A LaTex expression showing 2
b A LaTex expression showing 4
8
An svg image showing a math problem
Solve for the missing length on this triangle by completing the equilateral triangle
a A LaTex expression showing 1 over 2
b A LaTex expression showing 1