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

Level 1

This topic focuses on solving for missing lengths in 30-60-90 triangles using the properties of equilateral triangles and Pythagorean theorem. It is part of a broader unit on Pythagoras, intended for practice at a level 1 difficulty. The problems require knowledge of special right triangles and applying the Pythagorean theorem to find unknown side lengths. Each problem presents a different set of given values and asks to solve for the missing measurements, incorporating both standard numerical answers and those involving square roots.

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 Medium Side Worksheet

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Triangles (30/60/90) With Equilateral Guide - Hypotenuse to Medium Si...
1
An svg image showing a math problem
Solve for the missing length using Pythagoras and the equilateral triangle
a A LaTex expression showing \frac{5square root of 3}{2}
b A LaTex expression showing \frac{5square root of 2}{2}
2
An svg image showing a math problem
Solve for the missing length using Pythagoras and the equilateral triangle
a A LaTex expression showing 2square root of 3
b A LaTex expression showing 2square root of 2
3
An svg image showing a math problem
Solve for the missing length using Pythagoras and the equilateral triangle
a A LaTex expression showing 3square root of 3
b A LaTex expression showing 3
4
An svg image showing a math problem
Solve for the missing length using Pythagoras and the equilateral triangle
a A LaTex expression showing \frac{3square root of 2}{2}
b A LaTex expression showing \frac{3square root of 3}{2}
5
An svg image showing a math problem
Solve for the missing length using Pythagoras and the equilateral triangle
a A LaTex expression showing 3square root of 2
b A LaTex expression showing 3square root of 3
6
An svg image showing a math problem
Solve for the missing length using Pythagoras and the equilateral triangle
a A LaTex expression showing 1
b A LaTex expression showing \frac{square root of 3}{2}
7
An svg image showing a math problem
Solve for the missing length using Pythagoras and the equilateral triangle
a A LaTex expression showing \frac{7square root of 3}{2}
b A LaTex expression showing 7 over 2
8
An svg image showing a math problem
Solve for the missing length using Pythagoras and the equilateral triangle
a A LaTex expression showing 2
b A LaTex expression showing 2square root of 3