Special Right Triangles

Right-triangle methods for special right triangles.

Lesson 2 of 53 parts Practice Flashcards

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45-45-90 Triangles

Objective: Apply 45-45-90 triangles.

A 45-45-90 triangle has side ratio 1:1:√2.

Worked examples

Try itA 45-45-90 triangle has each leg 3. Find its hypotenuse.Show answer

3√2. Hypotenuse = leg×√2.

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Objective: Apply 45-45-90 triangles.

A 45-45-90 triangle has side ratio 1:1:√2.

Worked examples

Try itA 45-45-90 triangle has each leg 3. Find its hypotenuse.Show answer

3√2. Hypotenuse = leg×√2.

Objective: Apply 30-60-90 triangles.

A 30-60-90 triangle has opposite-side ratio 1:√3:2.

Worked examples

Try itA 30-60-90 triangle has short leg 4. Find the hypotenuse.Show answer

8. The hypotenuse is twice the short leg.

Objective: Apply recognizing special ratios.

Match angle position to the appropriate short leg, long leg, and hypotenuse.

Worked examples

Try itIn a 30-60-90 triangle, which side is opposite the 60° angle when short leg is 3?Show answer

3√3. The longer leg is √3 times the short leg.

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