Pythagorean Theorem & Classify Triangles by Angles & Sides

Pythagorean Theorem & Trigonometry Challenge: Real-World Applications

Grades: 8th–11th

Concepts Covered:

1. Converse of the Pythagorean Theorem

• Determine if triangles are acute, right, or obtuse using side lengths.

• Real-world example: “A triangular garden has sides 7 m, 2 4 m, and 2 5 m. Is it a right triangle?”

1. Classify Triangles by Angles & Sides

• Identify , acute, obtuse, or right triangles.

• Example: “A triangle has angles 3 0 , 6 0 , and 9 0 . Classify it by angles and sides.”

1. Pythagorean Theorem Word Problems

• Solve real-life scenarios (ladders, kites, navigation).

• Example: “A 2 6-ft ladder leans against a building, touching 1 0 ft up. How far is the ladder s base from the wall?”

1. Law of Sines & Cosines

• Find missing sides/angles in non-right triangles.

• Example: “Two ships leave port at 3 0 and 4 5 angles. How far apart are they after 1 0 miles?”

1. Pythagorean Theorem in 3 D

• Calculate space diagonals(rooms, cubes, pyramids).

• Example: “Find the longest pole that fits in a 5 m x 1 2 m x 4 m room.”

1. Solve a Right Triangle

• Find missing sides and angles using trig ratios (S OH-CA H-TO A).

• Example: “A right triangle has legs 9 cm and 1 2 cm. Find the hypotenuse and smallest angle.”

Why Teachers Love This Bundle:

Engaging Word Problems Connects math to architecture, sports, and construction.

Scaffolded Difficulty Starts with basics, progresses to 3 D and trig challenges.

Answer Key Included Step-by-step solutions with visual diagrams.

C C SS & T E KS A l i g n e d Covers 8.G.B.7, H S G-S RT.C.8, and H S G-MG.A.1.

Perfect for:

• Homework

• Stations/Centers

• Test Prep

• STEM Projects