Tech Math: Square Roots & Right Angled Triangles

 

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Relevant Material: "Square roots and right-angled triangles are applied in many fields, such as construction, engineering, and navigation, to solve problems involving distance, elevation, and ensuring right angles. For example, the Pythagorean theorem (

$a^2+b^2=c^2$

) uses square roots to calculate the length of one side of a right-angled triangle when the other two are known. This is used to determine the shortest distance between two points, measure the height of objects, or ensure a structure is square. 

Applications in real-world scenarios 

• Construction and engineering: Carpenters and engineers use right triangles to ensure walls are perpendicular, build rafters, and calculate the diagonal length of a structure or ramp.
• Navigation: The theorem helps calculate the shortest distance between two points, such as a ship sailing north and then east.
• Measurement: It is used to measure the height of tall objects like trees or buildings indirectly by using their shadow.
• Accident investigation: Police can estimate a vehicle's speed by measuring the length of its skid marks and using the square root in a formula.
• Finance: Square roots are used to calculate the rate of return on an investment over a two-year period. 

How square roots are used with right-angled triangles 

• Finding the hypotenuse: To find the longest side (
  

  $c$
  ) of a right triangle, you add the squares of the other two sides (
  

  $a$
  and
  

  $b$
  ) and then take the square root of the sum:
  

  $c=\sqrt{a^2+b^2}$
  .
• Finding a leg: To find the length of one of the other sides (e.g.,
  

  $b$
  ), you subtract the square of one leg from the square of the hypotenuse and then take the square root of the result:
  

  $b=\sqrt{c^2-a^2}$
  .
• Trigonometry: Square roots appear frequently in trigonometric calculations, such as finding the sine, cosine, or tangent of an angle in a right-angled triangle.." (Google) 

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