Math Problem Statement

Find the missing side x in the right triangle where the hypotenuse is 10, one leg is 6, and the other leg is x.

Solution

The given image represents a right triangle ABC\triangle ABC where:

  • AB=xAB = x (unknown)
  • AC=6AC = 6 (one leg)
  • BC=10BC = 10 (hypotenuse)

We can use the Pythagorean Theorem to find xx:

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

Substituting the given values:

x2+62=102x^2 + 6^2 = 10^2

x2+36=100x^2 + 36 = 100

x2=64x^2 = 64

x=64=8x = \sqrt{64} = 8

Thus, x=8x = 8.

Would you like a step-by-step explanation?

Here are five related questions you might find interesting:

  1. How do you determine if a given triangle is a right triangle using the Pythagorean theorem?
  2. What is the perimeter of the given triangle?
  3. How do you find the area of this triangle?
  4. If the triangle were scaled up by a factor of 2, what would its new dimensions be?
  5. How can trigonometric functions like sine, cosine, and tangent be applied to this triangle?

Tip:

Always check whether a triangle satisfies the Pythagorean theorem before assuming it is a right triangle!

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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 7-9