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Trigonometric Functions on Right Triangles quiz #2

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  • How do you find the approximate value of the difference between two angles given their measures?
    Subtract the smaller angle from the larger angle and round to the nearest degree if needed.
  • How do you find the measure of an angle in a triangle if you know the trigonometric ratio?
    Use the appropriate inverse trigonometric function (arcsin, arccos, or arctan) with the given ratio.
  • How do you find the measure of an angle in a trapezoid if you know the other angles?
    Subtract the sum of the known angles from 360 degrees to find the unknown angle.
  • How do you find the measure of an angle in a circle given the arc or central angle?
    The measure of the central angle is equal to the measure of the arc it intercepts.
  • How do you find the measure of an angle in a triangle if you know the trigonometric ratio?
    Use the inverse trigonometric function (arcsin, arccos, or arctan) with the given ratio.
  • Which pair of angles is supplementary?
    Two angles are supplementary if their measures add up to 180 degrees.
  • If the measure of an arc is (4x – 18) degrees, how do you find the value of x if the arc's measure is known?
    Set (4x – 18) equal to the known arc measure and solve for x.
  • Given a right triangle JKM, how do you write the trigonometric ratios for angle J?
    For angle J, sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent.
  • Which trigonometric ratios are correct for triangle ABC?
    sin(A) = opposite/hypotenuse, cos(A) = adjacent/hypotenuse, tan(A) = opposite/adjacent.
  • If triangle ABC is similar to triangle DBE, what can you say about their corresponding angles?
    Corresponding angles of similar triangles are congruent.
  • How do you find the measure of an angle in a kite if you know the other angles?
    Use the fact that the sum of the angles in a quadrilateral is 360 degrees and subtract the known angles from 360.
  • If angle PSR measures 99 degrees, what is the measure of angle PSQ if they are supplementary?
    Angle PSQ = 180 - 99 = 81 degrees.
  • Which equation can be used to solve for side c in a right triangle given an angle and another side?
    Use c = known side / trigonometric ratio, depending on which sides and angle are given.
  • How do you find the value of an angle if you know its supplement is 52 degrees?
    The angle is 180 - 52 = 128 degrees.
  • If each exterior angle of a regular decagon has a measure of (3x + 6) degrees, how do you find the value of x?
    Set (3x + 6) × 10 = 360 and solve for x.
  • How do you find the measure of an angle in a triangle if you know the trigonometric ratio?
    Use the appropriate inverse trigonometric function (arcsin, arccos, or arctan) with the given ratio.
  • If two triangles are similar and you know two corresponding angles, how do you find the third angle?
    Subtract the sum of the two known angles from 180 degrees to find the third angle.
  • If two angles in a triangle are 34 degrees and 26 degrees, what is the measure of the third angle?
    The third angle is 180 - 34 - 26 = 120 degrees.
  • How do you find the length of a minor arc in a circle given the radius and central angle?
    Arc length = (central angle/360) × 2πr.
  • If angle MLO measures 112 degrees, what is the measure of its supplement?
    The supplement is 180 - 112 = 68 degrees.
  • How do you find the measure of the smallest angle in a triangle if you know all three angles?
    Identify the angle with the smallest degree measure.
  • What is the ratio of the area of a sector to the area of the entire circle if the sector's central angle is θ degrees?
    The ratio is θ/360.
  • If a line is tangent to a circle at point K and the radius is drawn to K, what is the relationship between the tangent and the radius?
    The tangent is perpendicular to the radius at the point of tangency.
  • Which expressions can be used to find the measure of angle BAC in a right triangle?
    arccos(adjacent/hypotenuse), arcsin(opposite/hypotenuse), arctan(opposite/adjacent).
  • How do you find the approximate length of an arc in a circle given the radius and central angle in degrees?
    Arc length = (central angle/360) × 2πr.
  • Which congruency theorem can be used to prove that two triangles are congruent if all three sides are equal?
    The Side-Side-Side (SSS) congruence theorem.
  • In triangle QRS, how do you find the sine of angle Q?
    sin(Q) = length of side opposite Q / hypotenuse.
  • If the measure of arc ED is 68 degrees, what is the measure of the inscribed angle EFD that intercepts it?
    The inscribed angle EFD is half the arc, so 68/2 = 34 degrees.
  • Which expressions can be used to find the measure of angle BAC in a right triangle?
    arccos(adjacent/hypotenuse), arcsin(opposite/hypotenuse), arctan(opposite/adjacent).
  • If angle MNO measures 112 degrees, what is the measure of its supplement?
    The supplement is 180 - 112 = 68 degrees.
  • How do you find the degree measure of an angle in a triangle using trigonometric ratios?
    Use the appropriate inverse trigonometric function (arcsin, arccos, or arctan) with the given side lengths.
  • 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.
  • If two parallel lines are cut by a transversal and one angle is 31 degrees, what is the measure of the corresponding angle on the other parallel line?
    The corresponding angle is also 31 degrees.
  • How do you find the approximate difference between two angles given their measures?
    Subtract the smaller angle from the larger angle and round to the nearest degree if needed.
  • How do you find the measure of an angle in a triangle if you know the trigonometric ratio?
    Use the appropriate inverse trigonometric function (arcsin, arccos, or arctan) with the given ratio.
  • If two lines are parallel and a transversal creates alternate interior angles, what is the relationship between those angles?
    Alternate interior angles are congruent.
  • Which angle is a vertical angle with angle EFD?
    The angle directly across from EFD at the intersection point is its vertical angle.
  • In which triangle is the value of x equal to arccos(4.3/6.7)?
    In a right triangle where the side adjacent to angle x is 4.3 units and the hypotenuse is 6.7 units, x = arccos(4.3/6.7).
  • How do you find the measure of an angle in a triangle if you know the trigonometric ratio?
    Use the appropriate inverse trigonometric function (arcsin, arccos, or arctan) with the given ratio.
  • How do you find the measure of an angle in a triangle if you know the trigonometric ratio?
    Use the appropriate inverse trigonometric function (arcsin, arccos, or arctan) with the given ratio.