Math Problem Statement

What is the length of the hypotenuse? If necessary, round to the nearest tenth.

Solution

To determine the length of the hypotenuse cc in this right triangle, we use the Pythagorean Theorem:

c2=a2+b2c^2 = a^2 + b^2

Here, both legs of the triangle are 7mi7 \, \text{mi}. Substituting these values:

c2=72+72c^2 = 7^2 + 7^2

c2=49+49c^2 = 49 + 49

c2=98c^2 = 98

Now take the square root of both sides:

c=98c = \sqrt{98}

Approximating this:

c9.9mic \approx 9.9 \, \text{mi}

Thus, the length of the hypotenuse is 9.9 miles.


Would you like a detailed explanation of the steps or have further questions?

Here are 5 related questions for further practice:

  1. What is the hypotenuse of a right triangle with legs 5 mi and 12 mi?
  2. How does the Pythagorean Theorem apply to different types of right triangles?
  3. If one leg is 6 mi and the hypotenuse is 10 mi, how do you calculate the other leg?
  4. What are some real-life applications of the Pythagorean Theorem?
  5. How do you determine if a triangle is a right triangle using side lengths?

Tip: Always double-check your calculations when applying the Pythagorean Theorem, especially when dealing with square roots!

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles

Formulas

Pythagorean Theorem

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9