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

Level 1

This math topic focuses on solving for missing lengths in 30/60/90 triangles by employing an equilateral triangle construction. As a specialized application of the Pythagorean theorem, each problem presents diagrams of triangles, asking learners to determine specific side lengths based on established relationships in these special right triangles. The skills practiced include identifying different sides of a right triangle (hypotenuse, medium side), applying square root operations, and using fractional expressions to solve for lengths. Additionally, this topic aligns with foundational geometry concepts and trigonometric ratios.

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 Side to Hypotenuse Worksheet

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Triangles (30/60/90) With Equilateral Guide - Medium Side to Hypotenu...
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 7
b A LaTex expression showing \frac{7square root of 3}{2}
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 2square root of 3
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 4
b A LaTex expression showing 2square root of 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 3
b A LaTex expression showing \frac{3square root of 2}{2}
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 5
b A LaTex expression showing \frac{5square root of 2}{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
b A LaTex expression showing \frac{3square root of 2}{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 \frac{7square root of 3}{2}
b A LaTex expression showing 7