IA2.GR.B.6: Justify the side length relationships in special right triangles (30°-60°-90° and 45°-45°-90°). a. Use geometric reasoning (e.g., dissecting an equilateral triangle or square) to explain why the side length relationship in special right triangles hold. b. Describe the consistent ratios of side lengths in these triangles (e.g., 1:1:√2 and 1:√3:2), and explain how these ratios relate to the angle measures.

Justify the side length relationships in special right triangles (30°-60°-90° and 45°-45°-90°). a. Use geometric reasoning (e.g., dissecting an equilateral triangle or square) to explain why the side length relationship in special right triangles hold. b. Describe the consistent ratios of side lengths in these triangles (e.g., 1:1:√2 and 1:√3:2), and explain how these ratios relate to the angle measures.

Example Problems

A volleyball coach tapes a

30\text{-}60\text{-}90

triangle on the gym floor to mark a serving drill. The shorter leg (across from the

30^\circ

angle) is

5\text{ feet}

long. How long is the longer leg?

Write your answer in simplest radical form.

A cheerleading squad paints a

30^\circ\text{-}60^\circ\text{-}90^\circ

triangle on the mat to mark a stunt position. The shorter leg (across from the

30^\circ

angle) is

7\text{ feet}

long. How long is the longer leg?
Write your answer in simplest radical form.

A roof pitch on a soccer team's equipment shed is designed as a

30\degree\text{-}60\degree\text{-}90\degree

triangle. The shorter leg (across from the

30\degree

angle) is

4\text{ feet}

long. How long is the longer leg?
Write your answer in simplest radical form.

1-on-1 AI tutoring aligned to IA2.GR.B.6. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →