Show that Lobachevsky's basic triangle formulas transform into standard formulas of spherical trigonometry if one replaces the sides a,b,c of the triangle by ia,ib,ic respectively. Assume C is a right angle.

Q: Consider the triangle AABC with sides a 5 and b = 4, and ZA = 120°. Use the Law of Sines to…

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Q: at is the name of the three-dimensional shape formed if points M and N remain fixed, while line…

A: Here we have to write the name of the three-dimensional shape formed if points M and N remain fixed,…

Q: What is the spherical excess of a spherical triangle whose angles are all right angles

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Q: To test for symmetry with respect to the origin,what should you replace?

A: To test for symmetry with respect to origin we replace x by -x and y by -y. If after simplifying the…

Q: Can a right triangle be constructed whose sides measure (show work): 22) 9m, 12m, 15m 23) 5ft, 12ft,…

A: 22) Yes, that is possible, cf. the converse Pythagorean theorem, which says that any triangle with…

Q: 7) Classify the triangle with side lengths: 8, 13, 20 * Acute Right Obtuse

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Q: In spherical geometry, draw a triangle with three right angles. What is the area of the triangle?

A: A globe is the best visualization tool. It will make a triangle in certain senses, because of having…

Q: In spherical geometry, draw a triangle with three right angles in the spherical model with radius r.…

A: Given that,In a spherical geometry,A triangle has three right angles with radius r.The length of…

Q: let A=(2,1) B=(0, sqrt(5)) and C= (0,1) show that the sum of the hyperbolic angles of triangle ABC…

A: Given - let A=(2,1) B=(0, sqrt(5)) and C= (0,1) To show - Show that the sum of the hyperbolic angles…

Q: Prove that the mid-points of the sides of any triangle form a triangle similar to the original…

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Q: What are all the angles of rotation that will map a regular pentagon onto itself?

A: A pentagon has 5 sides and a complete about origin is of 3600.

Q: a spherical triangle where one angle is greater than 90 degrees

A: Spherical triangle is said to be right if only one of its included angle is equal to 90°. Triangles…

Q: A 12-foot ladder leans against a building. The top of theladder leans against the wall 10.5 feet…

A: Consider a right triangle with an angle, x, other than right angle. Take the length of side opposite…

Q: Consider the triangle AABC with sides a = 5 and b = 4, and ZA = 120°. Use the Law of Sines to…

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Q: Convert the following point from spherical to rectangular coordinates: 4π 11π (8,36 471, 117).

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Q: Triangle FXY is rotated and then translated to a new location and named triangle ABC. Which of the…

A: Given  ∆FXY is rotated and translated to a new location and named ∆ABC.

Q: In spherical geometry, draw a triangle with three right angles. How long are the sides of this…

A: Triangle with three right angles is shown in the image below

Q: is 6, 8,10 make sides of a right angle triange?

A: Use pythagorous theorem to check.

Q: Consider a right triangle with right angle C. If b= 32ft andc- 51ft, find all missing sides and…

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Q: 7. Escher was an artist who accidentally incorporated non-Euclidian geometry into his work. True or…

A: THE STATEMENT IS ABSOLUTELY TRUE M C ESCHER WAS A DUTCH ARTIST AND HE MANAGED TO REPRESENT MANY…

Q: Is a triange with the verticies A(7,1) B(0,4) and C(-4,-8) a right triangle yes or no?

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Q: Tell which triangle congruence theorem is used to prove the triangles congruent.

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Q: Solve for the missing sides using pythagorean theorem or special right triangle rules. 15 :: 5/3 :…

A: Given here we have given the right angle triangle  we name it right angled  ∆ABC we have to find…

Q: Your friend claims that the SAS Congruence Theorem (Theorem 5.5) will apply to a triangle and its…

A: We know by the SAS congruence theorem Two sides and the included angle of one triangle are…

Q: Plot the image of triangle AABC under a reflection across line l. A.

A: The Answer is : Reflection Rule : Reflection Over X Axis. When reflecting over (across) the x-axis,…

Q: Is it possible to draw a two-sided polygon in spherical geometry?  Please explain your answer.

A: Two sided polygon in spherical geometry is possible or not?

Q: CONSTRUCT EQUILATERAL TRIANGLE UPON AB AS THE BASE. At

A: According to question given thatAB is the base of the equilateral triangle and we have to construct…

Q: Aregular pentagon is shown

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Q: Find the angle formed by the intersection of a face diagonal t the diagonal of a cube drawn from the…

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Q: Show that the points (a, a).(-a,-a) and (-3a, 3a) are the vertice of an equilateral triangle.Also,…

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Q: How can we apply the Pythagorean theorem to the reference right triangle?

A: The Pythagorean theorem states that the if the length of the two sides of the triangle are known,…

Q: When a hexagonal figure with equal sides is rotated, then the angle of rotation is _________.

A: Known fact: Angle of rotation is the smallest angle in which the figure is turned to make it look…

Q: Show that triangle with vertices p(6,-7),q(11,-3) and R(2,-2) is a right angled triangle using…

A: We first find the length of the sides using the distance formula.…

Q: If RS = 40, ST = 41, and RT = 11, is ARST a right triangle? Explain. %3D %3D %3D

A: Check by Pythagorean theorem

Q: In spherical geometry, draw a triangle with three right angles. What fraction of the surface of the…

A: Given that, In spherical geometry, a triangle is drawn with three right angles. To find the fraction…

Q: 1. Of the triangles with sides 11, 5, 9 or with sides 6, 10, 8; which is a right triangle? In figuro…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Consider AABC and ADEF, both of which lie in the xy- coordinate plane. The pre-image, AABC, is…

A: Congruent triangles are defined when 2 triangles have equal corresponding sides and equal…

Q: What where the contributions that Euclid made to Geometry?

A: topic - Euclid's  geometry

Q: What are the coordinates of the image of Triangle ABC following a reflection over the line y = x.

A: Given data:   The coordinate of the point A is (x1, y1)=(-2,-1). The coordinate of the point B is…

Q: Pythagoras' Theorem is a rule that will work in any triangle that has

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Q: A triangle is inscribed in a rectangular hyperbola s to the opposite side. Prove that the trian…

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Q: What solid is formed when a right triangle is rotated around a line containing one of its legs? cone…

A: Shape problem....

Q: How does the law of cosines generalize the Pythagorean theorem?

A: We have to show that the law of cosines generalize the Pythagorean theorem.

Q: 2. An airplane travels 210 km on a straight Course, making an angle of 22.5° E of N. If then changes…

A: Given,  An airplane travels 210 k on a straight course, making an angle of 22.5 degree east of…

Q: What theorem can be used to prove that AABD ADCA? Explain by naming the corresponding parts of the…

A: We have different congruency theorem to prove the congruency of the two triangles.  Sum of them are…

Q: Select the triangle (in the correct order) and the method for which the two triangles shown are…

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Q: Consider the triangle ABD formed with the points A(1,-4), B(-4,1) and D(-3,-5). determine its…

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Q: What is the measure of the angle between the diagonal of a cube and the diagonal of the face of the…

A: Let's take 1,1,1 as the body diagonal vector b Let's take 1,1,0 as the face diagonal vector f Let's…