Math Problem Statement

correct answer

Find the missing segment in the right triangle where the hypotenuse is 26, one leg is 12, and the other leg is unknown.

Solution

To find the missing segment, labeled with a "?", we can use the Pythagorean theorem, as the image forms a right triangle.

Given:

  • Hypotenuse c=26c = 26
  • One leg a=12a = 12

The length of the missing segment, bb, can be found using the Pythagorean theorem formula: c2=a2+b2c^2 = a^2 + b^2

Calculation:

  1. Substitute the known values: 262=122+b226^2 = 12^2 + b^2
  2. Calculate the squares: 676=144+b2676 = 144 + b^2
  3. Rearrange to solve for b2b^2: b2=676144b^2 = 676 - 144 b2=532b^2 = 532
  4. Take the square root of both sides: b=53223.05b = \sqrt{532} \approx 23.05

Therefore, the missing segment bb is approximately 23.05.

Would you like further explanation on this?

Here are 5 related questions for further practice:

  1. How would the answer change if the hypotenuse was increased?
  2. What if the known leg was longer than the hypotenuse?
  3. Can the Pythagorean theorem apply to any triangle?
  4. How does this triangle relate to trigonometric ratios?
  5. How would you find the angles if all sides are known?

Tip: In right triangles, always check if you have two sides given to use the Pythagorean theorem effectively.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Pythagorean Theorem

Formulas

c^2 = a^2 + b^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10