Math Problem Statement

Using Pythagoras' theorem, calculate the length of YZ. Give your answer to 1 decimal place. The triangle has sides of 5 cm and 17 cm, with the third side being the unknown length YZ.

Solution

The question asks you to use the Pythagorean theorem to calculate the length of YZYZ, given the triangle has a right angle, and two sides are 5cm5 \, \text{cm} and 17cm17 \, \text{cm}. Let’s solve this step-by-step.

Pythagorean Theorem

c2=a2+b2c^2 = a^2 + b^2 Where cc is the hypotenuse (the longest side, opposite the right angle), and aa and bb are the other two sides.

  1. Identify sides:

    • Hypotenuse (cc): 17cm17 \, \text{cm}
    • One leg (aa): 5cm5 \, \text{cm}
    • Unknown (bb): YZYZ
  2. Rearrange the formula to find bb: b2=c2a2b^2 = c^2 - a^2

  3. Substitute values: b2=17252b^2 = 17^2 - 5^2 b2=28925b^2 = 289 - 25 b2=264b^2 = 264

  4. Solve for bb: b=26416.2cmb = \sqrt{264} \approx 16.2 \, \text{cm}

Final Answer

The length of YZYZ is approximately 16.2 cm (to 1 decimal place).

Would you like me to go over this in more detail or clarify anything?


Here are 5 related questions to expand on this:

  1. How would the Pythagorean theorem apply if the triangle had sides given in different units (e.g., meters instead of centimeters)?
  2. What are some real-world applications of the Pythagorean theorem in construction or navigation?
  3. Can the Pythagorean theorem be used in non-right triangles? Why or why not?
  4. What is the difference between a perfect square and the square root when solving for unknowns?
  5. How can you verify the accuracy of your calculation when using square roots?

Tip: Always double-check whether the given side is the hypotenuse when applying the Pythagorean theorem—it’s a common mistake to mix up the sides!

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangle
Pythagoras' Theorem

Formulas

c^2 = a^2 + b^2
b^2 = c^2 - a^2

Theorems

Pythagoras' Theorem

Suitable Grade Level

Grades 8-10