Math Problem Statement

For the following right triangle, find the side length x.

Solution

The image shows a right triangle with two known sides: 40 and 9, and the unknown side labeled xx, which we need to find.

We can use the Pythagorean Theorem to solve for xx, which is typically used for right triangles. The Pythagorean theorem states:

a2+b2=c2a^2 + b^2 = c^2

Where:

  • aa and bb are the legs of the triangle,
  • cc is the hypotenuse (the longest side, opposite the right angle).

From the image:

  • One leg =9= 9,
  • The other leg =x= x,
  • The hypotenuse =40= 40.

Substitute into the Pythagorean theorem:

x2+92=402x^2 + 9^2 = 40^2 x2+81=1600x^2 + 81 = 1600 x2=160081x^2 = 1600 - 81 x2=1519x^2 = 1519

Now, take the square root of both sides to solve for xx:

x=151938.98x = \sqrt{1519} \approx 38.98

So, the side length xx is approximately 38.98 units.

Would you like further clarification on any part of the solution? Here are five related questions you might find helpful:

  1. What conditions are necessary to apply the Pythagorean Theorem?
  2. Can the Pythagorean Theorem be used in non-right triangles?
  3. How can you check if a triangle is a right triangle given its sides?
  4. What other methods are there to find missing sides of triangles besides the Pythagorean Theorem?
  5. How can you find the angles in a right triangle if you know all the sides?

Tip: When applying the Pythagorean theorem, always make sure the hypotenuse is correctly identified as the longest side.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Algebra

Formulas

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

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10