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

Level 1

This math topic focuses on finding missing side lengths in 30-60-90 triangles by applying the Pythagorean theorem. It utilizes specific ratios characteristic of 30-60-90 triangles, where students learn to calculate either the hypotenuse or a shorter side based on given information. The problems progress through different levels of difficulty and require students to use their knowledge of triangle properties and algebraic manipulation. Each question is illustrated with a diagram, reinforcing both geometric visualization and algebraic solutions.

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

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

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