Math Problem Statement

Using Pythagoras' theorem, calculate the length of YZ. Give your answer to 1 d.p.

Solution

To calculate the length of YZYZ using Pythagoras' theorem:

In the right-angled triangle XYZXYZ:

  • XY=9cmXY = 9 \, \text{cm} (one side),
  • XZ=17cmXZ = 17 \, \text{cm} (the hypotenuse),
  • YZYZ is the unknown side.

Step-by-Step Solution:

Pythagoras' theorem states:

Hypotenuse2=Base2+Height2\text{Hypotenuse}^2 = \text{Base}^2 + \text{Height}^2

Rearranging to find the unknown side YZYZ:

XZ2=XY2+YZ2    YZ2=XZ2XY2XZ^2 = XY^2 + YZ^2 \implies YZ^2 = XZ^2 - XY^2

Substitute the values: YZ2=17292YZ^2 = 17^2 - 9^2

Simplify: YZ2=28981YZ^2 = 289 - 81 YZ2=208YZ^2 = 208

Take the square root: YZ=208YZ = \sqrt{208}

Using a calculator: YZ14.4cm(to 1 decimal place).YZ \approx 14.4 \, \text{cm} \, (\text{to 1 decimal place}).

Final Answer:

The length of YZYZ is 14.4 cm.


Would you like a breakdown of the steps or further clarification? Let me know!

Related Questions:

  1. How do you use Pythagoras' theorem in other right-angled triangles?
  2. What are the conditions for using Pythagoras' theorem?
  3. Can Pythagoras' theorem be applied in 3D shapes?
  4. How do you determine the hypotenuse of a triangle?
  5. What happens when the sides of a triangle do not satisfy Pythagoras' theorem?

Tip:

When solving for a missing side in a right triangle, always check that you correctly identify the hypotenuse (the longest side).

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Math Problem Analysis

Mathematical Concepts

Geometry
Right-Angled Triangles
Pythagoras' Theorem

Formulas

c^2 = a^2 + b^2

Theorems

Pythagoras' Theorem

Suitable Grade Level

Grades 7-9