Mr Hickman's Class 2022-2023
Mr Hickman does NOT participate in social media!
  • Home
    • About
    • CC Math Standards Page >
      • CC Functions
    • VIDEOS 2020-2021
    • Desmos Library Directory >
      • Desmos How to VIDEOS 1
      • Desmos: How Do I Library
      • Desmos Coordinate Geometry
      • Desmos Geometry
      • Algebra Desmos Library >
        • Lines and Linear Functions
      • Quadratics 101 >
        • Parabola 101: Vertex Form Function
        • Parabola 101: Vertex Form Relations
      • Desmos: Advanced Algebra >
        • Non Linear Systems
      • Desmos Trigonometry
      • Desmos PreCalculus >
        • Desmos: Absolute Value Function
        • Desmos: Piecewise Functions
        • Desmos Polar Coordinate System
      • Desmos: AP Calculus
    • Digital Resources: >
      • Digital Resources: Number Line, Lines, and Linear Systems
      • Geogebra Library Directory
      • TI Nspire Library Directory >
        • TI Nspire How to VIDEOS 1
      • YOU Tube Library Directory
      • KHAN Academy Library Directory
      • "Other" Websites Library Directory
    • Technology Tutorials >
      • Building a Weebly Page >
        • How to Use a Template page to add pages quickly
      • MS Teams Technology Tutorials
      • MS Whiteboard Technology Tutorials
      • Flip Grid Technology Tutorials
      • One Note Technology Tutorials
      • Small PDF Technology Tutorials
    • What calculator should I get?
    • SAT Review 2019 >
      • Complex Number Review
    • PC Documents
  • ALGEBRA
    • Power Practice
    • Radical Practice
    • Exponential Practice
    • Logarithm Practice
    • Logarithmic Practice
    • Rational Functions
  • Geometry
    • Geometry File Library
    • BOY Review: Solve Equations 1
    • Week 4 Geometry Enriched
    • Week 5 Geometry Enriched
    • Enriched Geometry Semester 1 Archive
  • PRE-CALC
  • AP PRE-CALC
  • AP CALC AB
    • AP Calculus Objectives from AP Central
    • AP Calc AB Exam Details & Prep
    • AP CALC AB UNIT 1
    • AP CALC AB UNIT 2
    • AP CALC AB UNIT 3
    • AP CALC AB UNIT 4
    • AP CALC AB UNIT 5
    • AP CALC AB UNIT 6
    • AP CALC AB UNIT 7
    • AP CALC AB UNIT 8
    • CALC AB WK 4 GP4
    • AP Calculus Worksheets
  • Data Prob Stats

What if you had two sides of a right triangle?


If you are only told that you have a pair of sides of a right triangle and nothing else, then you have TWO possible right triangles
  • leg/leg/unknown hypotenuse
    • find the sum of the squares of the given sides
    • take square root of the result
    • simplify radicals when asked to and capable
    • approximate when necessary
  • unknown leg/leg/hypotenuse
    • the hypotenuse MUST be the larger of the two given numbers!
    • find the difference of the squares  of the given sides 
    • take square root of the result
    • simplify radicals when asked to and capable
    • approximate when necessary
What if I have three sides of a triangle?
small/medium/large side was given
  • medium-small < large < medium + small OR NOT A triangle 
  • This is a case/result of the Triangle Inequality Theorem
  • if small and medium lead to hypotenuse, then four things could be true
    • hypotenuse > largest side
      • this means your triangle is an acute scalene triangle
    • hypotenuse > largest side and largest side is smaller than small + medium sides
      • ​this means that your triangle is an obtuse scalene triangle
    • SPECIAL CASE 1:
    • hypotenuse = largest side​
      • ​this means your triangle is an acute scalene triangle
    • SPECIAL CASE 2:
    • hypotenuse > largest side and largest side is larger than small + medium sides
      • ​this means that NO TRIANGLE EXISTS with these three side length​​

This assignment was an open ended assignment given in four parts 


Each group needs to: 
  • find the missing hypotenuse
  • write a range of values of a side that is larger than the hypotenuse that would still produce a triangle
  • write a range of values of a side that is larger than the hypotenuse that would still produce a triangle
  • classify the types of triangles that NON-hypotenuse lengths of a missing side of a triangle

Concepts:
  • Right triangles
  • Oblique triangles 
  • Pythagorean Theorem
  • Triangle Inequality Theorem 
Resources Web page Links
  • Oblique Triangle Definition
    • DEFINITION
    • DEFINITION
    • ​DEFINITION
  • ​ Math is Fun : TRIANGLE Link ​
  • Triangle Inequality Theorem Link
  • Pythagorean Theorem Link

Exploration 1
Row 1
  • 3/4
  • ​5/12
  • ​9/40
  • 7/25
Row 2
  • 9/11
  • 14/50
  • 27/123
  • 15/25
CLICK ON DESMOS LINK BELOW TO CHECK ANSWERS

Click on lower right-hand corner to check your answers


Row 3
  • 6/8/9
    • acute triangle because the largest side is smaller than its related right triangle's hypotenuse
    • scalene triangle because three different side lengths
    • best classification acute scalene
  • 6/8/10
    • THIS IS THE RIGHT triangle
    • Satisfies the Pythagorean Theorem's side relationships
    • Best classification right scalene triangle
  • 6/8/11
    • obtuse triangle because it is a triangle whose largest side exceeds the hypotenuse of the related right triangle
    • why is it a triangle at all?
      • the sum of 6 and 8 is 14 and the difference of 8 and 6 is 2
      • 2 < largest side < 14
    • best classification obtuse scalene
  • 6/8/15
    • NOT a triangle
    • WHY?
      • the sum of 6 and 8 is 14 and the difference of 8 and 6 is 2
      • largest side > 14

Row 1 Support 3/4/missing hypotenuse

Row 1 Support missing leg/3/4

Exploration 2

Row 1
  • 9/15
  • ​15/39
  • ​18/82
  • 30/50
Row 2
  • 6/8
  • ​6/12
  • ​18/20
  • 14/48

Row 3
  • 9/12/13
    • acute triangle because the largest side is smaller than its related right triangle's hypotenuse
    • scalene triangle because three different side lengths
    • best classification acute scalene
  • 9/12/15
    • THIS IS THE RIGHT triangle
    • Satisfies the Pythagorean Theorem's side relationships
    • Best classification right scalene triangle
  • 9/12/18
    • obtuse triangle because it is a triangle whose largest side exceeds the hypotenuse of the related right triangle
    • why is it a triangle at all?
      • the sum of 9 and 12 is 21 and the difference of 12 and 9 is 3
      • 3< largest side < 21
    • best classification obtuse scalene
  • 9/12/21
    • NOT a triangle
    • WHY?
      • the sum of 9 and 12 is 21 and the difference of 9 and 12 is 3
      • largest side = 21

Exploration 3

Row 1
  • 15/20
  • ​50/100
  • ​18/24
  • 27/45
Row 2
  • 27/36
  • ​75/180
  • ​36/160
  • 21/75

Row 3
  • 12/16/19
    • acute triangle because the largest side is smaller than its related right triangle's hypotenuse
    • scalene triangle because three different side lengths
    • best classification acute scalene
  • 12/16/20
    • THIS IS THE RIGHT triangle
    • Satisfies the Pythagorean Theorem's side relationships
    • Best classification right scalene triangle
  • 12/16/22
    • obtuse triangle because it is a triangle whose largest side exceeds the hypotenuse of the related right triangle
    • why is it a triangle at all?
      • the sum of 12 and 16 is 28 and the difference of 12 and 16 is 4
      • 4< largest side < 28
    • best classification obtuse scalene
  • 12/16/29
    • NOT a triangle
    • WHY?
      • the sum of 12 and 16 is 28 and the difference of 12 and 16 is 4
      • largest side = 29

Exploration 4

Row 1
  • 300/400
  • ​10/24
  • ​45/200
  • 175/625
Row 2
  • 8/15
  • ​24/51
  • ​45/90
  • 18/24

Row 3
  • 4/12/13
    • obtuse triangle because it is a triangle whose largest side exceeds the hypotenuse of the related right triangle
    • why is it a triangle at all?
      • the sum of 4 and 12 is 16 and the difference of 4 and 12 is 8
      • 8< largest side < 16
    • best classification obtuse scalene
  • 10/24/25
    • acute triangle because the largest side is smaller than its related right triangle's hypotenuse
    • scalene triangle because three different side lengths
    • best classification acute scalene
  • 15/36/39
    • THIS IS THE RIGHT triangle
    • Satisfies the Pythagorean Theorem's side relationships
    • Best classification right scalene triangle
  • 20/48/52
    • THIS IS THE RIGHT triangle
    • Satisfies the Pythagorean Theorem's side relationships
    • Best classification right scalene triangle

As a mathematics teacher, one person would have a hard time producing the amount of resources that the internet provides, so I supplement my resources with the assist of MANY other hard working and excellent mathematicians from the internet.  I will try my best to give them credit and thank them anonymously in total here.  I hope that others would visit and support their sites.  I try and avoid those that are attempting to sell their services because I am not trying to induce a profit or monetary support personally, but I respect their right to do so, just that I am not trying to enter into ADVERTISEMENT or REFERRAL business.

  • Easy Calculation.com
  • Clark University Website
    • Dave Joyce 
  • Math is Fun Website
Mr Hickman is available for assistance after school practically anytime.  Talk to me to be certain that I am aware you are coming and 99% of the time I will be able to help you