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

Gregory draws a scale drawing of his room. the scale that he uses is 1 cm : 4 ft. on his drawing, the room is 3 centimeters long. which equation can be used to find the actual length of gregory's room?

What is the simplified form of square root of 400 to the 100th power ?

Which scenarios are most effectively explored by conducting an experiment? there is more than one correct answer. select all that apply. researchers want to study the effectiveness of a particular drug for treating migraines. they want to know which dosage of the drug yields the best results with the least side effects. to ensure fair results, the researchers want to ensure that participants and dosage administrators do not know which dosage participants receive. a teacher wants to plan a class fieldtrip and quickly determine where students prefer to go for the class fieldtrip. a car mechanic wants to know which of two engine brands makes better-performing engines. he wants to test the engines in identical situations and rate their performance in a way that can be fairly measured. a chemist studies the properties of a metal compound. she wants to know how the sample size of the metal affects its ability to conduct electricity. she wants to conduct the research in a controlled environment to minimize bias. a realty company wants to know the average income of its clients. the company wants to gather data income from current clients.