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Trigonometric Functions on Right Triangles quiz #4

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  • If angle 1 = 61.8 degrees, what is the measure of its supplement?
    The supplement is 180 - 61.8 = 118.2 degrees.
  • If cos(B) = sin(A) and angle A = 32 degrees, what is the measure of angle B?
    Angle B = 90 - 32 = 58 degrees.
  • What is the value of secant θ given that secant is the reciprocal of cosine?
    sec(θ) = 1 / cos(θ).
  • How do you find the measures of two angles if their sum is known?
    Subtract the known angle from the total and assign the remainder to the other angle.
  • Which figure in a circle is a chord?
    A chord is a line segment with both endpoints on the circle.
  • If triangle ABC has the angle measures shown, what can you say about the sum of the angles?
    The sum of the angles in a triangle is always 180 degrees.
  • If triangle XYZ is isosceles and angle Y measures a degrees, what is the measure of angle X?
    If the triangle is isosceles with two equal angles, angle X = (180 - a) / 2.
  • If two parallel lines are cut by a transversal, what is the relationship between alternate interior angles?
    Alternate interior angles are congruent.
  • How do rays AB and AC form both a line and an angle?
    Rays AB and AC with a common endpoint form an angle; if they are collinear, they form a straight line.
  • If triangle RST is an acute triangle, what can you say about angle S?
    Angle S is less than 90 degrees.
  • What does the linear pair perpendicular theorem state?
    If two lines intersect to form a linear pair of congruent angles, the lines are perpendicular.
  • What is the longest side of a right triangle called?
    The hypotenuse.
  • In triangle LMN, if angle L + angle M = x degrees, what is angle N?
    Angle N = 180 - x degrees.
  • In a right triangle, for which acute angle are the sine and cosine ratios equal?
    For a 45-degree angle, sine and cosine are equal.
  • Given triangle JKL, which trigonometric function is equal to cos(52°)?
    cos(52°) = adjacent/hypotenuse for angle 52°.
  • What is the angle of elevation and depression in trigonometry?
    The angle of elevation is measured upward from the horizontal; the angle of depression is measured downward from the horizontal.
  • If the measure of arc AB is x degrees, what is the measure of angle AOB at the center?
    Angle AOB = x degrees.
  • How do you find the measure of an indicated angle in a triangle to the nearest degree?
    Use the appropriate inverse trigonometric function and round to the nearest degree.
  • If in triangle JKL, cos(K) = 24/51, what is the measure of angle K?
    Angle K = arccos(24/51).
  • How do you determine the cosine of an angle using a calculator?
    Enter the angle in degree or radian mode and use the cosine function on the calculator.
  • Are congruent angles always equal in measure?
    Yes, congruent angles have equal measures.
  • In a circle, if the length of an arc intercepted by a central angle is 12 mm, how do you find the central angle?
    Central angle = (arc length / circumference) × 360 degrees.
  • If the measure of an arc in a circle is 54 degrees, what is the measure of the central angle?
    The central angle is 54 degrees.
  • If in a circle, arc ED measures 17 degrees, what is the measure of the central angle that intercepts it?
    The central angle is 17 degrees.
  • If the measure of an arc in a circle is 40 degrees, what is the measure of the central angle?
    The central angle is 40 degrees.
  • If the measure of an arc in a circle is 68 degrees, what is the measure of the central angle?
    The central angle is 68 degrees.
  • If two parallel lines are cut by a transversal and one angle is 20 degrees, what is the measure of the corresponding angle?
    The corresponding angle is also 20 degrees.
  • If two triangles have congruent corresponding angles, what can you say about the triangles?
    The triangles are similar.
  • Given the side lengths of triangles PQR and STU, how do you determine which angle has a given sine ratio?
    The angle whose sine equals the ratio of the length of the side opposite the angle to the hypotenuse.
  • If two triangles have congruent corresponding angles, what can you say about the triangles?
    The triangles are similar.
  • In a right triangle, how do you find the sine of angle A?
    sin(A) = length of side opposite A / hypotenuse.
  • If two lines are parallel, which angle is congruent to a given angle formed by a transversal?
    The corresponding angle on the other parallel line is congruent.
  • 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 the measure of an angle at the center of a circle is 70 degrees, what is the measure of the corresponding arc?
    The arc measure is 70 degrees.
  • Given a right triangle with sides labeled, how do you find tan(θ)?
    tan(θ) = opposite/adjacent.
  • Which side of a triangle is adjacent to the reference angle and connected to the right angle?
    The adjacent side.
  • If the measure of angle 6 is 141 degrees, what is the measure of its supplement?
    The supplement is 180 - 141 = 39 degrees.
  • If angle BGC = (6x – 13) degrees and angle CGF = (4x + 3) degrees, how do you find angle BGF if the three angles form a straight line?
    Set (6x – 13) + (4x + 3) + angle BGF = 180 and solve for angle BGF.
  • What is the sine of an angle in a right triangle?
    Sine is the ratio of the length of the side opposite the angle to the hypotenuse.