Complete the proof of the Law of Sines/Cosines. Triangle ABC with side c between points A and B, side a between points B and C. Segment drawn from point B to point D where D is between points A and C, segment BD is labeled x. Given triangle ABC with altitude segment BD labeled x. Angles ADB and CDB are right angles by _1._, making triangle ABD and triangle BCD right triangles. Using the trigonometric ratios sine of A equals x over c and sine of C equals x over a. Multiplying to isolate x in both equations gives x = _2._ and x = a ⋅ sinC. We also know that x = x by the reflexive property. By the substitution property, _3._. Dividing each side of the equation by ac gives: sine of A over a equals sine of C over c.

1. definition of altitude
2. c ⋅ sinA
3. c ⋅ sinA = a ⋅ sinC
1. definition of right triangles
2. c ⋅ sinB
3. c ⋅ sinB = a ⋅ sinC
1. definition of right triangles
2. a ⋅ sinA
3. a ⋅ sinA = c ⋅ sinC
1. definition of altitude
2. c ⋅ sinA
3. a ⋅ sinA = c ⋅ sinC

Describe how the presence of possible outliers might be identified on the following. (a) histograms gap between the first bar and the rest of bars or between the last bar and the rest of bars large group of bars to the left or right of a gap higher center bar than surrounding bars gap around the center of the histogram higher far left or right bar than surrounding bars (b) dotplots large gap around the center of the data large gap between data on the far left side or the far right side and the rest of the data large groups of data to the left or right of a gap large group of data in the center of the dotplot large group of data on the left or right of the dotplot (c) stem-and-leaf displays several empty stems in the center of the stem-and-leaf display large group of data in stems on one of the far sides of the stem-and-leaf display large group of data near a gap several empty stems after stem including the lowest values or before stem including the highest values large group of data in the center stems (d) box-and-whisker plots data within the fences placed at q1 â’ 1.5(iqr) and at q3 + 1.5(iqr) data beyond the fences placed at q1 â’ 2(iqr) and at q3 + 2(iqr) data within the fences placed at q1 â’ 2(iqr) and at q3 + 2(iqr) data beyond the fences placed at q1 â’ 1.5(iqr) and at q3 + 1.5(iqr) data beyond the fences placed at q1 â’ 1(iqr) and at q3 + 1(iqr)