Mathematics
Grade 10
15 min
Special right triangles
Special right triangles
What you'll learn
- Identify the relationships between different customary units of volume (cups, pints, quarts, gallons) with 80% accuracy on a worksheet.
- Solve word problems involving converting between customary units of volume (cups, pints, quarts, gallons) with 70% accuracy.
- Explain the process of converting a larger customary unit of volume (e.g., gallons) to a smaller unit (e.g., cups) in writing, using correct mathematical vocabulary, in at least two out of three attempts.
- Apply their knowledge of customary volume conversions to solve real-world word problems involving measurement of liquids with at least 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify 45-45-90 and 30-60-90 triangles based on their angle measures or side length properties.
Recall and state the constant side length ratios for both 45-45-90 and 30-60-90 triangles.
Calculate the lengths of two missing sides of a special right triangle when given the length of one side.
Solve for side lengths that require rationalizing the denominator.
Apply the properties of special right triangles to solve multi-step geometric problems.
Connect the side ratios of special right triangles to the sine, cosine, and tangent of 30°, 45°, and 60° angles.
Model and solve real-world problems using special right triangles.
Ever wondered how builders can find the exact length for a diagonal brace without complex calculations? 📐 They use the power of spec...
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Key Concepts & Vocabulary
TermDefinitionExample
45-45-90 TriangleAn isosceles right triangle where the two acute angles are both 45 degrees. The two legs are always congruent.A square cut in half along its diagonal creates two 45-45-90 triangles.
30-60-90 TriangleA right triangle with acute angles of 30 and 60 degrees. The side lengths are all different and follow a specific ratio.An equilateral triangle cut in half by an altitude creates two 30-60-90 triangles.
LegsThe two sides of a right triangle that form the 90-degree angle.In a right triangle with sides a, b, and c, if angle C is 90°, then sides a and b are the legs.
HypotenuseThe longest side of a right triangle, located opposite the 90-degree angle.In a right triangle with sides a, b, and c, if angle C is 90°, then side c is the hypotenuse.
Short Leg (30-6...
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Core Formulas
45-45-90 Triangle Theorem
Legs = x, Hypotenuse = x\sqrt{2}
In a 45-45-90 triangle, the two legs are congruent. The length of the hypotenuse is the length of a leg multiplied by the square root of 2.
30-60-90 Triangle Theorem
Short Leg = x, Long Leg = x\sqrt{3}, Hypotenuse = 2x
In a 30-60-90 triangle, the hypotenuse is twice the length of the short leg. The long leg is the length of the short leg multiplied by the square root of 3.
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Challenging
The area of a 45-45-90 triangle is 32 square units. What is the length of its hypotenuse?
A.8√2 units
B.8 units
C.16 units
D.4√2 units
Challenging
A square with side length 6 is positioned adjacent to an equilateral triangle with side length 6. What is the total height of the combined figure from the base of the square to the top vertex of the triangle?
A.12
B.6 + 6√3
C.6 + 3√2
D.6 + 3√3
Challenging
The vertices of a right triangle are at (0,0), (5,0), and (0,y). If the hypotenuse is 10, what kind of special right triangle is it?
A.45-45-90
B.30-60-90
C.It is not a special right triangle
D.Cannot be determined
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Frequently asked questions
What grade level is "Special right triangles"?
Special right triangles is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Special right triangles?
You'll be able to: Identify the relationships between different customary units of volume (cups, pints, quarts, gallons) with 80% accuracy on a worksheet; Solve word problems involving converting between customary units of volume (cups, pints….
Is "Special right triangles" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Special right triangles?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.