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

Level 1

This math topic focuses on solving problems related to 30/60/90 triangles using properties derived from equilateral triangles. The primary skill practiced involves determining the missing lengths of sides in these specific right triangles by extending them into equilateral triangles, which aids in applying the Pythagorean theorem and trigonometric ratios efficiently. Multiple examples are included in the material to demonstrate the necessary calculations for both the hypotenuse and the shorter side, ensuring a comprehensive understanding of the relationships within 30/60/90 triangles.

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 - Hypotenuse to Short Side Worksheet

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Triangles (30/60/90) With Equilateral Guide - Hypotenuse 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 1 over 2
b A LaTex expression showing \frac{square root of 2}{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 3 over 2
b A LaTex expression showing 3
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 3square root of 2
b A LaTex expression showing 3
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 5
b A LaTex expression showing 5 over 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 \frac{5square root of 2}{2}
b A LaTex expression showing 5 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 1
b A LaTex expression showing square root of 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 3
b A LaTex expression showing 3square root of 3
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 3square root of 2
b A LaTex expression showing 3