Trigonometric Functions on Right Triangles quiz #4 Flashcards
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). Which of the following statements are true according to the tangent function? tan(θ) = opposite/adjacent; tan(θ) = sin(θ)/cos(θ); tan(θ) is undefined for θ = 90°. 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.
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