Right Triangles and Trigonometry flashcards

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How do you find the hypotenuse of a right triangle from its legs?Pythagorean Theorem: c = √(a² + b²): square the legs, add them, then take the square root.
How do you find a missing leg of a right triangle?Pythagorean Theorem: a = √(c² − b²): subtract the square of the known leg from the square of the hypotenuse.
How can you tell whether three side lengths form a right triangle?Pythagorean Theorem: Check whether a² + b² = c², where c is the longest side. If so, the triangle is right.
What are the side ratios in a 45°–45°–90° triangle?Special Right Triangles: 1 : 1 : √2. The legs are equal and the hypotenuse is a leg times √2.
What are the side ratios in a 30°–60°–90° triangle?Special Right Triangles: Short leg : long leg : hypotenuse = 1 : √3 : 2.
In a special right triangle, how do you tell which side is which?Special Right Triangles: First see which angle a side faces; that tells you whether it is the short leg, long leg, or hypotenuse.
What is the sine of an acute angle in a right triangle?Sine, Cosine, and Tangent: sin θ = opposite ÷ hypotenuse.
What is the cosine of an acute angle in a right triangle?Sine, Cosine, and Tangent: cos θ = adjacent ÷ hypotenuse.
What is the tangent of an acute angle in a right triangle?Sine, Cosine, and Tangent: tan θ = opposite ÷ adjacent.
How do you find an unknown side of a right triangle using trig?Solving Right Triangles: Label the sides around the known angle, choose the ratio with your known side and missing side, then solve.
How do you find an unknown acute angle of a right triangle?Solving Right Triangles: Form a side ratio, then use the inverse trig function, such as θ = tan⁻¹(opposite ÷ adjacent).
How are the two acute angles of a right triangle related?Solving Right Triangles: They are complementary; they add to 90°.
What is an angle of elevation?Applications of Trigonometry: The angle measured upward from the horizontal to an object above the viewer.
What is an angle of depression?Applications of Trigonometry: The angle measured downward from the horizontal to an object below the viewer.
How do you set up a height-and-distance word problem with trig?Applications of Trigonometry: Sketch the height and horizontal distance as the legs of a right triangle before choosing sine, cosine, or tangent.