### 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°.*

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

To the nearemainder foot, recognize and state just how far the ship traveled from suggest A to suggest D.

**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 feet

**33.**

*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.

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**34.**

*In the diagram below, AC = DF and also points A, C, D, and F are colstraight on line ℓ.*

**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.*

See more: Which Of The Following Would Probably Not Be Determined Using Managerial Accounting Reports?

Prove ABCD is a rhombusYou 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

See more: Which Of The Following Would Probably Not Be Determined Using Managerial Accounting Reports?

Prove ABCD is a rhombus

**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?*