A mapmaker has successfully mapped Carlisle Street and River Avenue, as shown in the diagram. The last step is to map Beacon Street correctly. To save time, the mapmaker intends to measure just one more angle or side of the triangle. Which angle(s) or side(s) could the mapmaker measure to be sure that only one triangle is possible? For each angle or side that you name, justify your answer. Suppose that instead of measuring the length of Carlisle Street, the mapmaker measured ∠A and ∠C along with ∠B. Would the measures of the three angles alone assure a unique triangle? Explain.

The base of a triangle exceeds the height by 7 centimeters. if the area is 400 square centimeters, find the length of the base and the height of the triangle.

Points a, b, and c form a triangle. complete the statements to prove that the sum of the interior angles of triangle abc is 180

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.