YouVocabulary and Concepts ANSWER!Determine whether each statement is True or False.1. It is possible to solve a triangle if the only given information consists of the measures of the three angles of the triangle.. In general, it is not possible to use the 2 lengths of all the sides. Law of Sines to solve a triangle for which we are given the3. Given ∆ABC with A = 30°, c = 3 cm, and a = 2.5 cm. There can be more than one triangle with the given dimensions that can be drawn. 4. In a scalene triangle, the largest angle is always the opposite the longest side and the smallest angle is always the opposite teh shortest side.5. Given ∆ABC with a A = 57°, a = 15m, and c = 20 m. There is no triangle for these values
Question
YouVocabulary and Concepts ANSWER!Determine whether each statement is True or False.1. It is possible to solve a triangle if the only given information consists of the measures of the three angles of the triangle.. In general, it is not possible to use the 2 lengths of all the sides. Law of Sines to solve a triangle for which we are given the3. Given ∆ABC with A = 30°, c = 3 cm, and a = 2.5 cm. There can be more than one triangle with the given dimensions that can be drawn. 4. In a scalene triangle, the largest angle is always the opposite the longest side and the smallest angle is always the opposite teh shortest side.5. Given ∆ABC with a A = 57°, a = 15m, and c = 20 m. There is no triangle for these values
Solution
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False. Knowing the measures of the three angles of a triangle is not enough to solve the triangle. You also need to know at least one side length.
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True. The Law of Sines can be used to solve a triangle if we are given the lengths of all the sides.
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True. This is a case of the Ambiguous Case for the Law of Sines, where two different triangles could be drawn with the given dimensions.
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True. In a scalene triangle, the largest angle is always opposite the longest side and the smallest angle is always opposite the shortest side.
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False. Using the Law of Sines, we can find that sin(B) = (sin(A)*c)/a = (sin(57)*20)/15 = 1.14, which is not possible because the range of the sine function is -1 to 1. Therefore, there is no triangle with these values.
Similar Questions
Which statements are true?Select each correct answer.ResponsesAll triangles have 3 sides that are equal in length.All triangles have 3 sides that are equal in length.Only some triangles have 1 right angle.Only some triangles have 1 right angle.All triangles are polygons.All triangles are polygons.All triangles have 3 angles.All triangles have 3 angles.All triangles are open figures.
36 of 5536 of 55 Items36:43 Skip to resourcesQuestionGiven the following three measures of angles or sides, determine if it is possible to construct a unique triangle, more than one triangle, or no triangle.sides 5 inches, 8 inches, and 15 inchesResponsesA no triangleno triangleB a unique trianglea unique triangleC more than one trianglemore than one triangleD the answer cannot be determined
TriangleGet the lengths of three sides of a triangle. Check whether the triangle can be formed or not. If possible then classify the triangle as equilateral, isosceles or scalene. If unable to form the triangle (the sum of the lengths of any two sides of a triangle must be greater than the length of the third side) print error. An equilateral triangle is a type of triangle that has all three sides of equal length.An isosceles triangle is a type of triangle that has at least two sides of equal length.A scalene triangle is a type of triangle that has all three sides of different lengths.
Which of the following can be used to find the measure of an angle of a triangle when the lengths of the sides are known?*a. Law of Sinesb. Law of Cosinesc. Law of Inertiad. Law of Entropy
If two triangles are congruent, which of the following statements must be true? Check all that apply.A.The triangles have the same size, but not the same shape.B.The corresponding sides of the triangles are congruent.C.The corresponding angles of the triangles are congruent.D.The triangles have the same size and shape.
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