Math Problem Statement

Find the hypotenuse of a right triangle with legs of length 4 and 7.

Solution

The image you provided appears to be a right triangle with one of the angles being a right angle (90°). The two given side lengths are 7 and 4. It seems you're looking for the third side, which is likely the hypotenuse.

To find the length of the hypotenuse, we can use the Pythagorean theorem, which states:

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

where:

  • aa and bb are the lengths of the two legs of the triangle,
  • cc is the length of the hypotenuse.

Here, a=4a = 4 and b=7b = 7. Let's calculate the hypotenuse cc:

c=42+72c = \sqrt{4^2 + 7^2} c=16+49c = \sqrt{16 + 49} c=65c = \sqrt{65}

Thus, the length of the hypotenuse is approximately:

c8.06c \approx 8.06

If you have any other questions or need further clarification, feel free to ask!

Would you like to explore these topics further?

  1. How to calculate the area of a right triangle.
  2. Understanding the Pythagorean theorem in more detail.
  3. How to use the Pythagorean theorem for different types of triangles.
  4. The relationship between trigonometric functions and right triangles.
  5. How to apply the Pythagorean theorem to real-life problems.

Tip: You can always check if a triangle is a right triangle by using the Pythagorean theorem to see if a2+b2=c2a^2 + b^2 = c^2 holds true.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Pythagorean Theorem

Formulas

a² + b² = c²

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9