4. A contractor is preparing a bid for a new roof. In the current plans, the roof rises at an angle of 38 degrees, and the house is 30 feet across the front and 45 feet deep. If the client wants to increase the rise of the roof by 4 degrees to have a steeper roof, how much will the area of the roof increase or decrease? If the average cost to install a new roof is about $7 per square foot, what is the difference in cost for the steeper roof? 5. A pilot is flying from Austin, Texas, to Jacksonville, Florida, which is due east of Austin. To avoid a headwind from the jet stream, the pilot changes course by turning the plane 17 to the south for 800 miles. He then makes a turn of 67 toward the northeast to head to Jacksonville. a. How far does the pilot need to travel after the 67 turn to get to Jacksonville? b. How much farther did the pilot have to fly to avoid the jet stream? 6. When/how is the Law of Sines useful? 7. Do you think this works for any triangle? Why/Why not