Here are the questions, via answers and explacountries, for the New York State Geomeattempt (Usual Core) Regents exam, Parts 3 and also 4. Tbelow were 3 concerns in Part 3, each worth 4 credits. There were 2 inquiries in Part 4, each worth 6 credits. Partial credit may be earned. All work-related need to be presented. In basic, a correct answer without any work-related is worth 1 credit, unmuch less that answer is offered as a choice and an explanation is forced.Link to Part 1Link to Part 2

Part 3

32. As shown in the diagram below, a ship is heading straight toward a lightresidence whose beacon is125 feet above sea level. At the first sighting, point A, the angle of elevation from the ship to the light was 7°. A brief time later, at allude D, the angle of elevation was 16°.
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To the nearemainder foot, recognize and state just how far the ship traveled from suggest A to suggest D.
Label DC as x and also AC as y. To find ADVERTISEMENT, you must discover (y - x). You have angles and also the opposite side. You need to uncover the surrounding side. As such, you need to usage tan. Make certain your calculator is in DEGREE mode!tan(16) = 125/x, x = 125/tan(16) = 435.9268...tan(7) = 125/y, y = 125/tan(7) = 1018.0433...Subtract y - x = 1018.0433 - 435.9268 = 582.1165 = 582 feet33. Triangle ABC has actually vertices via A(x,3), B(-3,-1), and C(-1,-4). Determine and also state a worth of x that would make triangle ABC a best triangle. Justify why triangle ABC is a appropriate triangle.

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On the graph, plot points B and C. Keep in mind that the slope of BC is -3/2. (You have the right to usage the formula or just compose it out.) Keep in mind that the slope of AB should be 2/3 to be perpendicular. Go up 2 over 3, make a allude at (0, 1). Repeat up 2 over 3, make a allude at (3, 3). Label this A. Draw a line from A to C. You have actually a ideal triangle. State that x = 3.NOTE: you can rather have actually AC via a slope of 2/3. In that case, point A will not be a totality number. If you use suggest C and also the slope to uncover the equation of the line, you can discover point A, which would be (9.5, 3), making x = 9.5.34. In the diagram below, AC = DF and also points A, C, D, and F are colstraight on line ℓ.
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Let triangle D"E"F" be the photo of triangle DEF after a translation alengthy ℓ, such that point D is mapped onto suggest A. Determine and also state the location of F. Explain your answer.Let triangle D"E"F" be the image of triangle DEF after a reflection across line ℓ. Suppose that E is located at B. Is triangle DEF congruent to triangle ABC? Exsimple your answer.
First: Point F" would certainly be at point C after the translation. Because AC = DF and also DF = D"F", if D" is at point A then F" have to be at suggest C.Second: If E"" lays on suggest B, then by SSS ABC = D""E""F"". Because the translation and also the reflection are rigid movements which carry out not influence the size or form of the figure, D""E""F"" = DEF. Thus ABC = DEF. (Note: Eextremely equal authorize (=) in this paragraph must be a "congruent" symbol.)

Part 4

35. In the diagram of parallelogram ABCD below, BE ⊥ CED, DF ⊥ BFC, and CE = CF.

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Prove ABCD is a rhombus
You deserve to write this as a two-column proof or a paragraph. Look at triangles BEC and also DEF. (Highlight them if is provides it simpler to watch.) Each triangle has actually a ideal angle. CF is congruent to CE (given). Angle C is congruent to itself (reflexive). By ASA, triangle BEC = DFC. Because of this, BC is congruent to CD by CPCTC. By interpretation, a parallelogram via 2 consecutive congruent sides is a rhombus.36. Walter desires to make 100 candles in the form of a cone for his brand-new candle company. The mold presented listed below will certainly be offered to make the candles. Each mold will have actually a elevation of 8 inches and a diameter of 3 inches. To the nearemainder cubic inch, what will be the complete volume of 100 candles?
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