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Trigonometric Functions on Right Triangles quiz #5 Flashcards

Trigonometric Functions on Right Triangles quiz #5
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  • If the measure of angle 6 is 32 degrees, what is the sum of the measures of angles 4 and 5 if they form a straight line?
    The sum is 180 - 32 = 148 degrees.
  • What is the tangent ratio for an angle in a right triangle?
    Tangent is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
  • How many sides does a regular polygon have if each interior angle measures 160 degrees?
    n = 360 / (180 - 160) = 18 sides.
  • How many sides does a polygon have if the sum of the interior angles is 1080 degrees?
    n = (1080/180) + 2 = 8 sides.
  • How many sides does a regular polygon have if each interior angle measures 144 degrees?
    n = 360 / (180 - 144) = 10 sides.
  • If sin(θ) = x, what is the value of csc(θ)?
    csc(θ) = 1 / sin(θ).
  • If three lines intersect to form a triangle, how do you find the value of an angle x?
    Use the fact that the sum of the angles in a triangle is 180 degrees and solve for x.
  • Which trigonometric ratio is calculated by dividing the length of the side opposite an angle by the length of the hypotenuse?
    The sine ratio.
  • Given right triangle DEF, what is the value of sin(E)?
    sin(E) = length of side opposite E / hypotenuse.
  • Given right triangle XYZ, what is the value of tan(60°)?
    tan(60°) = √3.
  • What is the measure of each angle of a regular 22-gon? Round to the nearest tenth if necessary.
    Each angle is [(22-2) × 180] ÷ 22 ≈ 163.6 degrees.
  • If a transversal cuts parallel lines and angle 4 = 55.1°, what are the measures of angles 5 and 7?
    Angles 5 and 7 are also 55.1° (corresponding and alternate interior angles).
  • How do you find the measure of an arc in a circle given the central angle?
    The measure of the arc in degrees is equal to the measure of the central angle.
  • How do you find the exact values of the six trigonometric ratios of an angle in a right triangle?
    Use the side lengths: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent, csc(θ) = hypotenuse/opposite, sec(θ) = hypotenuse/adjacent, cot(θ) = adjacent/opposite.