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

Level 1

This math topic focuses on solving for missing lengths in 30-60-90 triangles, particularly transitioning from the hypotenuse to the short side. It includes questions that apply the Pythagorean Theorem, specifically adapted for this type of right triangle, which splits an equilateral triangle into two. Each problem displays the triangle and provides formulaic answers (such as square root expressions and fractional values). This set of problems is geared towards learners practicing to understand the geometric properties and relationships of 30-60-90 triangles within the broader context of Pythagoras' theorem.

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

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

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