A passenger in an airplane at an altitude of 10 kilometers sees two towns directly to the east of the plane. The angles of depression to the towns are 25° and 55° (see figure). How far apart are the towns? (Round your answer to one decimal place.) 55° 25° 10 km **** Not drawn to scale

Distance Suppose Figure 22 is an exaggerated diagram of a plane flying above earth. If the plane is 4.55 miles above earth and the radius of earth is 3.960 miles, how far is it from the plane to the horizon? What is the measure of angle A? Figure 22

Albert lives in New Orleans. At noon on a summer day, the angle of elevation of the sun is 84. The window in Alberts room is 4.0 feet high and 6.5 feet wide. (Sec Figure 24.) a. Calculate the area of the floor surface in Alberts room that is illuminated by the sun when the angle of elevation of the sun is 84. b. One winter day the angle of elevation of the sun outside Alberts window is 37. Will the illuminated area of the floor in Alberts room be greater on the summer day, or on the winter day? Figure 24

Laying Phone Cable City A lies on the north bank of a river that is 1 mile wide. You need to run a phone cable from City A to City B, which lies on the opposite bank 5 miles down the river. You will lay L miles of the cable along the north shore of the river, and from the end of that stretch of cable you will lay W miles of cable running under water directly toward City B. See Figure 2.108. Figure 2.108 You will need the following fact about right triangles: A right triangle has two legs, which meet at the right angle, and the hypotenuse, which is the longest side. An ancient and beautiful formula, the Pythagorean theorem, relates the lengths of the three sides: Lengthofhypotenuse=Lengthofoneleg2+Lengthofotherleg2 a. Find an appropriate right triangle that shows that W=1+(5L)2 b. Find a formula for the length of the total phone cable P from City A to City B as a function of L. c. Make a graph of the total phone cable length P as a function of L, and explain what the graph is showing. d. What value of L gives the least length for the total phone cable? Draw a picture showing the least-length total phone cable.