Math Problem Statement

Find the length of the third side of the right triangle with one leg measuring 7 and the hypotenuse measuring 24. Round to the nearest tenth if necessary.

Solution

To find the length of the third side of the right triangle, we can apply the Pythagorean Theorem, which is expressed as:

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

Where aa and bb are the two legs of the right triangle, and cc is the hypotenuse.

Given:

  • The first leg is 7.
  • The hypotenuse is 24.

We are looking for the second leg. Let’s denote it as bb.

Using the Pythagorean Theorem:

72+b2=2427^2 + b^2 = 24^2

Simplifying:

49+b2=57649 + b^2 = 576

Now, solve for b2b^2:

b2=57649b^2 = 576 - 49 b2=527b^2 = 527

Now, take the square root of both sides to find bb:

b=527b = \sqrt{527}

Calculating the square root:

b22.9b \approx 22.9

Thus, the length of the third side is approximately 22.9 units, rounded to the nearest tenth.

Would you like a more detailed explanation, or do you have any other questions?

Here are some related questions for further exploration:

  1. What happens if you change one of the triangle's side lengths?
  2. How does the Pythagorean Theorem apply to non-right triangles?
  3. Can the Pythagorean Theorem be used in 3D geometry?
  4. How do trigonometric ratios relate to right triangles?
  5. What are the conditions for a triangle to be classified as a right triangle?

Tip: Always remember to double-check whether the triangle is a right triangle before using the Pythagorean Theorem.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Pythagorean Theorem

Formulas

a^2 + b^2 = c^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 6-8