Optimization with angles. A drainage canal is constructed so its cross section isshaped like a trapezoid with equally sloping sides. If the bottom and sides each have length 5 feet, what angle θ would yield the greatest cross-sectional area?

A 42m lighthouse sits on the shore of a body of water. From the top of the lighthouse, a worker can see a cruise ship and yacht on the water, separated by an angle of 103 degrees from her viewpoint. The angle of elevation from the cruise ship to the top of the lighthouse is 38 degrees, and the angle of elevation from the yacht to the top of the lighthouse is 31 degrees. How far apart are the ships to the nearest metre?

A billboard at ground level has a support length of 26 feet that extends from the top of the billboard to the ground. A post that is 5 feet tall is attached to the support and is 4 feet from where the base of the support is attached to the ground. In the figure shown, the distance, in feet, from the base of the billboard to the base of the support is labeled z. billboard 26 post Assuming the post and bill board are parallel to each other (and perpendicular to the ground) we can prove the smaller triangle is similar to the larger triangle by [ Select ] Using the given information along with pythagorean theorem and proportions, x = [ Select ]

In Billy Jay Joe Bob's family, the birthday person always gets to cut the first piece of cake. Billy Jay is celebrating his birthday with both of his parents, his three brothers, and his girlfriend. He cuts his slice of cake with an 96° central angle. (The cake has a 10-inch radius) If the rest of the party equally shares the remaining portion of the cake, what is the approximate area that each one receives? Hint: How many people will be sharing the rest of the cake represented by the SHADED sector. Let pi = 3.14 and round your final answer to the nearest tenth. 10inches 96