Multiple Choice
Which of the following is a type of special right triangle commonly studied in trigonometry?
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2. Trigonometric Functions on Right Triangles
Special Right Triangles
Multiple Choice
In a special right triangle, if each leg has length , what is the length of the hypotenuse?
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Verified step by step guidance1
Recognize that the triangle described is a 45°-45°-90° special right triangle, which is an isosceles right triangle where the two legs are congruent.
Recall the property of a 45°-45°-90° triangle: the hypotenuse is equal to the leg length multiplied by \( \sqrt{2} \). This comes from the Pythagorean theorem applied to the legs of equal length.
Write the Pythagorean theorem for the triangle: \( \text{hypotenuse}^2 = x^2 + x^2 \), where \( x \) is the length of each leg.
Simplify the equation: \( \text{hypotenuse}^2 = 2x^2 \).
Take the square root of both sides to solve for the hypotenuse: \( \text{hypotenuse} = x \sqrt{2} \).
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