Find the area of triangle abc. round your answer to the nearest tenth. m∠a= 52°, a = 9.71, c = 9.33
a. 44.5 c. 49.4 b. 33.6 d. 77.1

The area of the Δ = 44.5 units² ⇒ answer (a)

Step-by-step explanation:

∵ a = 9.71 , c = 9.33 , m∠A = 52°

To find the area of the triangle we must have:

m∠B or b

By using sin Rule:

∵ a/sin∠A = c/sin∠C

∴ 9.71/sin52 = 9.33/sinC

∴ sinC = (9.33 × sin52) ÷ 9.71 = 0.757172

∴ m∠C = 49.2°

∴ m∠B = 180 - 52 - 49.2 = 78.8°

∵ A the Δ = 1/2 × a × c × sinB

∴ A = 1/2 × 9.71 × 9.33 × sin78.8 = 44.5 units² ⇒ answer (a)

I am not 100% sure, but just thinking about it logically, they should not be independent events, and I believe it is A.

Step-by-step explanation:

The reason I believe they are not independent events is because people in California may be used to eating a certain flavor pallet in their area, whereas Texas may have different general flavors in their area. Now as far as the numbers, I am not entirely sure, I am assuming you know since your question was just asking if they were independent or not. However, if it is percent, it does seem like A makes the most sense in relation to the totals. Also you can use deductive reasoning. Most often when there are answer choices, there is one correct answer choice, and the others have all the same aspects, but only 1 thing is changed. Since this is generally the case, you can take similarities between answer choices as parts that are correct, and the little variances which are only in one answer as modifications from the correct answer. For instance in this question, there is 1 that says yes, and 2 that say no. Because of this, I assume that it must be no since yes must be that one modification that makes that answer choice incorrect. Now its A or B. I look at all the answer choices and see that B is the only one that says California brand B is .36 whereas the other two say .55. From this I assume that .36 is the variance that makes it incorrect, leaving me with A as my answer.