Math Problem Statement

What is the length of hypotenuse c in a right triangle with legs of length 9 units and 12 units?

Solution

This is a right triangle problem where the lengths of two sides are given, and we are tasked with finding the hypotenuse cc.

We can solve this using the Pythagorean theorem, which states: c2=a2+b2c^2 = a^2 + b^2 Where aa and bb are the legs of the triangle, and cc is the hypotenuse.

In this case:

  • a=9a = 9
  • b=12b = 12

Now, let's compute the value of cc:

c2=92+122=81+144=225c^2 = 9^2 + 12^2 = 81 + 144 = 225 c=225=15c = \sqrt{225} = 15

Thus, the length of the hypotenuse cc is 15 units.

Would you like further details on this, or have any other questions?

Related Questions:

  1. How does the Pythagorean theorem apply to non-right triangles?
  2. What happens if both legs of the triangle are equal? How does it affect the hypotenuse?
  3. Can the Pythagorean theorem be applied to triangles in three-dimensional geometry?
  4. How would you find the area of the triangle given its sides?
  5. How do you calculate the sine, cosine, and tangent for this triangle?

Tip:

In right triangles, the Pythagorean theorem is only valid when dealing with 90-degree angles. Always ensure the triangle is right-angled before applying it.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangle
Pythagorean Theorem

Formulas

c^2 = a^2 + b^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9