Questions and Answers
What is the Pythagorean Theorem used for?
If $c^2 = a^2 + b^2$, then the triangle is right.
True
If $c^2 < a^2 + b^2$, then the triangle is acute.
True
If $c^2 > a^2 + b^2$, then the triangle is obtuse.
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What are the side ratios of a 45-45-90 right triangle?
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What are the side ratios of a 30-60-90 right triangle?
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What is trigonometry?
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What is sine?
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What is cosine?
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What is tangent?
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Study Notes
Pythagorean Theorem
- Utilized to determine the missing side length in a right triangle.
- Legs of the triangle are designated as A and B; C is the hypotenuse.
- Formula: ( a^2 + b^2 = c^2 ).
Identifying Triangle Types
- Right Triangle: Occurs when ( c^2 = a^2 + b^2 ).
- Acute Triangle: Characterized by ( c^2 < a^2 + b^2 ).
- Obtuse Triangle: Identified when ( c^2 > a^2 + b^2 ).
Special Right Triangles
- 45 - 45 - 90 Triangle: Ratio of the sides is 1:1:( \sqrt{2} ).
- 30 - 60 - 90 Triangle: Side length ratios are 1:( \sqrt{3} ):2.
Trigonometry
- Focuses on the measurements of triangles, including side lengths and angles.
Trigonometric Ratios
- Sine: Ratio of the length of the opposite side to the hypotenuse.
- Cosine: Ratio of the length of the adjacent side to the hypotenuse.
- Tangent: Ratio of the length of the opposite side to the adjacent side.
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Description
Test your understanding of the Pythagorean theorem, the different types of triangles, and special right triangles. This quiz explores trigonometric ratios and their applications in solving for side lengths and angles in triangles.
