Multiple Choice
In a unit circle, what is the measure in degrees of the central angle that corresponds to of a circle?
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2. Trigonometric Functions on Right Triangles
Special Right Triangles
Multiple Choice
In a triangle, if the length of each leg is , what is the length of the hypotenuse?
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Verified step by step guidance1
Recognize that a 45°-45°-90° triangle is an isosceles right triangle, meaning the two legs are congruent and the angles opposite those legs are both 45°.
Recall the special property of a 45°-45°-90° triangle: the hypotenuse is \( \sqrt{2} \) times the length of each leg.
Let the length of each leg be \( x \). Then, the hypotenuse \( h \) can be expressed as \( h = x \times \sqrt{2} \).
Use the Pythagorean theorem as a verification step: \( h = \sqrt{x^2 + x^2} = \sqrt{2x^2} = x\sqrt{2} \).
Conclude that the length of the hypotenuse in a 45°-45°-90° triangle with legs of length \( x \) is \( x\sqrt{2} \).
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