Special Right Triangles
Special right triangles in Grade 8 Saxon Math Course 3 include the 45-45-90 and 30-60-90 triangles, which have fixed side length ratios that allow quick calculation of unknown sides without the Pythagorean Theorem. The 45-45-90 triangle has legs in ratio 1:1:square root of 2, and the 30-60-90 triangle has sides in ratio 1:square root of 3:2. Students recognize these triangles in geometric figures and apply their ratios to solve problems efficiently.
Key Concepts
New Concept Two special right triangles, the 45 45 90 and the 30 60 90, have constant side length ratios. All 45 45 90 triangles have side lengths in the ratio of $1:1:\sqrt{2}$, and all 30 60 90 triangles have side lengths in the ratio of $1:\sqrt{3}:2$. What’s next This card is just the foundation. Next, you'll apply these ratios in worked examples to find missing side lengths and solve real world geometry puzzles involving area and distance.
Common Questions
What are special right triangles?
Special right triangles are the 45-45-90 and 30-60-90 triangles, which have fixed side ratios that make them easier to work with than general right triangles.
What are the side ratios of a 45-45-90 triangle?
The sides are in ratio 1:1:square root of 2. If the legs are each x, the hypotenuse is x times square root of 2.
What are the side ratios of a 30-60-90 triangle?
The sides are in ratio 1:square root of 3:2. The side opposite 30 degrees is the shortest, the side opposite 60 degrees is square root of 3 times the short side, and the hypotenuse is twice the short side.
When do you use special right triangle ratios instead of the Pythagorean Theorem?
Use special right triangle ratios when you recognize a 45-45-90 or 30-60-90 triangle from its angles. The ratios are faster than the Pythagorean Theorem for these specific cases.
How are special right triangles covered in Saxon Math Course 3?
Saxon Math Course 3 introduces special right triangles in the context of geometry problem solving, connecting them to square roots and the Pythagorean Theorem.