Math Problem Statement

Use the Pythagorean theorem to find the missing side of a right triangle with legs of lengths 1 and 4, and express the answer in simplified radical form.

Solution

In the uploaded image, you're asked to use the Pythagorean theorem to find the length of a side of a right triangle in simplified radical form. The triangle has sides labeled as follows:

  • One leg is 1 unit
  • The other leg is 4 units
  • The hypotenuse is the side we are solving for.

To apply the Pythagorean theorem, c2=a2+b2c^2 = a^2 + b^2, where cc is the hypotenuse and aa and bb are the other two sides. Plugging in the given values:

c2=12+42c^2 = 1^2 + 4^2 c2=1+16c^2 = 1 + 16 c2=17c^2 = 17

Thus, the hypotenuse cc is: c=17c = \sqrt{17}

This is already in simplified radical form. Would you like to go through the calculation details or have any other questions on this topic? Here are some related topics you might find interesting:

  1. How can you determine if a triangle is a right triangle using side lengths?
  2. What is the Pythagorean theorem and how is it derived?
  3. Can the Pythagorean theorem be applied to non-right triangles under any circumstances?
  4. How do you simplify radicals further when possible?
  5. Examples of real-life applications of the Pythagorean theorem.

Tip: To check if your triangle side lengths correctly apply to the Pythagorean theorem, simply substitute them into the equation and see if the equality holds. This also helps verify if it's a right triangle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Pythagorean Theorem
Radicals

Formulas

Pythagorean theorem: c^2 = a^2 + b^2

Theorems

Pythagorean theorem

Suitable Grade Level

Grades 8-10