Either Missing Length - Labelled Sides (Radical) (Level 2)

This math topic focuses on the Pythagorean Theorem, specifically finding either of the missing side lengths (labelled as a, b, or c) of a right triangle. The problems require expressing the missing side's length as a square root value. It covers a variety of problem scenarios centered around understanding and applying the theorem \(a^2 + b^2 = c^2\) to compute the length of a side when the other sides are given. Each question is designed to enhance proficiency in solving equations involving radicals in the context of geometry. The practice level is introductory, as it aims at building foundational skills in using the Pythagorean Theorem.

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Pythagorean Theorem - Either Missing Length - Labelled Sides (Radical) Worksheet

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Pythagorean Theorem - Either Missing Length - Labelled Sides (Radical)
1
An svg image showing a math problem
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
a A LaTex expression showing c=square root of 75
b A LaTex expression showing c=square root of 125
2
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=square root of 669
b A LaTex expression showing b=square root of 311
c A LaTex expression showing b=square root of 507
d A LaTex expression showing b=square root of 115
3
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing c=square root of 51
b A LaTex expression showing c=square root of 149
c A LaTex expression showing c=square root of 249
d A LaTex expression showing c=square root of -51
4
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing c=square root of -105
b A LaTex expression showing c=square root of 105
c A LaTex expression showing c=square root of 137
5
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=square root of 459
b A LaTex expression showing b=square root of 290
c A LaTex expression showing b=square root of 628
d A LaTex expression showing b=square root of 48
6
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing c=square root of 153
b A LaTex expression showing c=square root of 117
c A LaTex expression showing c=square root of 45
7
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=square root of 407
b A LaTex expression showing b=square root of 607
c A LaTex expression showing b=square root of 238
d A LaTex expression showing b=square root of 69
8
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=square root of 69
b A LaTex expression showing b=square root of 238
c A LaTex expression showing b=square root of 269
d A LaTex expression showing b=square root of 407