Trigonometric Functions on Right Triangles quiz #3 Flashcards
Trigonometric Functions on Right Triangles quiz #3
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Which expressions can be used to find the measure of angle ABC in a right triangle? arccos(adjacent/hypotenuse), arcsin(opposite/hypotenuse). How do you find the approximate length of a minor arc in a circle given the radius and central angle? Arc length = (central angle/360) × 2πr. Which expressions can be used to find the measure of angle ABC in a right triangle? arccos(adjacent/hypotenuse), arcsin(opposite/hypotenuse). If two lines are parallel and a transversal creates corresponding angles, what is the relationship between those angles? Corresponding angles are congruent. If two angles are congruent, what can you say about their measures? Congruent angles have equal measures. How do you find the value of the radius if you know the circumference of a circle? Radius = circumference / (2π). Which coordinates for points A' and B' would help prove that lines AB and A'B' are perpendicular? If the slopes of AB and A'B' are negative reciprocals, the lines are perpendicular. If x = 12 cm in a right triangle, how do you find the other sides using trigonometric ratios? Use the appropriate trigonometric ratio and the given angle to solve for the other sides. How do you find the measure of an angle if you know its supplement is 77 degrees? The angle is 180 - 77 = 103 degrees. How do you find the measures of two angles in a triangle if you know the third angle? Subtract the known angle from 180 degrees and divide the remainder as needed based on the triangle's properties. Can the tangent constraint be applied between a line and an arc? Yes, a tangent to a circle is perpendicular to the radius at the point of tangency. How do you find the approximate length of a minor arc in a circle given the radius and central angle? Arc length = (central angle/360) × 2πr. 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. What is the reciprocal of tan(β) in a right triangle? The reciprocal of tan(β) is cot(β) = adjacent/opposite. Which trigonometric functions have a domain of [-1, 1]? The sine and cosine functions have a domain of [-1, 1] for their range, but their domain is all real numbers. In triangle QRS, if the angle measures are given, how do you identify the obtuse angle? The obtuse angle is the one with a measure greater than 90 degrees. Which of the following angle measurements might you find in a right triangle? In a right triangle, one angle is 90 degrees and the other two are acute (less than 90 degrees). If h = 8.1 inches and k = 9 inches in a right triangle, how do you find the trigonometric ratios? Use the definitions: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent. If angle ATB = 20 degrees, what is the measure of its supplement? The supplement is 180 - 20 = 160 degrees. How do you find the perimeter of a rhombus given the length of one side? Perimeter = 4 × side length. 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 one angle of a right triangle measures 60 degrees, what is the measure of the other acute angle? The other acute angle is 90 - 60 = 30 degrees. If the angle bisector of angle PQR is QE and angle PQE = 2n degrees, what is the measure of angle PQR? Angle PQR = 2 × (2n) = 4n degrees. If angle VUW = (4x + 6) degrees and angle WUT = (6x – 10) degrees, how do you find x if the angles are supplementary? Set (4x + 6) + (6x – 10) = 180 and solve for x. Which of the following are exterior angles of a polygon? Exterior angles are formed by extending one side of the polygon at each vertex. If triangle ABC is rotated 100 degrees counterclockwise about a point, what is the measure of the corresponding angle in the image? The measure of the angle remains the same after rotation. In which triangle is the value of x equal to arctan(opposite/adjacent)? In a right triangle where the side opposite angle x and the side adjacent to x are known, x = arctan(opposite/adjacent). 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 AD is the altitude to BC in a triangle, what is the relationship between the sides and angles? The altitude creates two right triangles within the original triangle. If angle BGF = 152 degrees, what is the measure of its supplement? The supplement is 180 - 152 = 28 degrees. If angle CBD has a measure of 140 degrees, what is the measure of angle ABD if they are supplementary? Angle ABD = 180 - 140 = 40 degrees. If angle CED = 72 degrees and angle AEB = (7x – 2) degrees, how do you find x if the angles are supplementary? Set 72 + (7x – 2) = 180 and solve for x. What term describes a pair of vertical angles that are also supplementary? A pair of vertical angles that are supplementary are right angles (each 90 degrees). Which ratio gives the cosine of angle B in a right triangle? cos(B) = adjacent/hypotenuse. If two parallel lines are crossed by a transversal, what is the relationship between alternate interior angles? Alternate interior angles are congruent. What is the cosine ratio of angle XZW in a right triangle? cos(XZW) = adjacent/hypotenuse. What is the measure of each angle in a regular polygon with 6 sides? Each angle is [(6-2) × 180] ÷ 6 = 120 degrees. How many sides does a regular polygon have if each interior angle measures 177 degrees? Use the formula: n = 360 / (180 - 177) = 120 sides. If point Z is equidistant from the sides of triangle RST, what must be true? Point Z is the incenter of the triangle. If one angle of a right triangle measures 80 degrees, what is the measure of the other acute angle? The other acute angle is 90 - 80 = 10 degrees.
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