Completed_9.1_Jan30

Unit 9 Notes: Right Triangles and Trigonometry

Section 9.1: Pythagorean Theorem

• Think About It:

  • Activity: Trace eight right triangles using Patty Paper, cut them out, and discover how many can fit into a large square formed by the hypotenuse.

  • Importance: Understand how this activity models the Pythagorean Theorem.

• Essential Question:

  • Why does the Pythagorean Theorem work?

Finding the Missing Side of a Right Triangle

• Pythagorean Theorem:

  • For a right triangle with legs a and b, and hypotenuse c:

    [ a^2 + b^2 = c^2 ]

• Example Problems:

  • a. 3, 4, ______

  • b. 5, _____, 13

  • c. _____, 24, 25

• Pythagorean Triples:

  • Sets where a, b, and c are all whole numbers.

Types of Triangles

1. Determine Triangle Type (acute, right, obtuse):

   • Examples:

     • a. 11 in, 20 in, 23 in

     • b. 4 ft, 5 ft, 6 ft

     • c. 39 cm, 65 cm, 52 cm

     • d. 11 cm, 18 cm, 34 cm

2. Tree Problem:

   • A tree's stump is 7 feet tall and the top of the tree rests 24 feet away from it. Calculate the original height of the tree.

3. Calculate Area of Rectangle:

   • Understand how areas relate to the Pythagorean Theorem.

4. Pythagorean Theorem Applications:

   • If ( c^2 > a^2 + b^2 ) => obtuse triangle.

   • If ( c^2 < a^2 + b^2 ) => acute triangle.

Triangle Perimeter and Area

5. Shaded Triangle:

   • Find both the perimeter and area.

6. House Roof Design Problem:

   • Each side of the roof is 24 feet.

   • Questions to answer:

     • a. Approximate width (w) of the house?

     • b. Approximate height (h) of the roof above the ceiling?