Part 332. 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°.
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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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 435. 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?