867 CHAPTER 8 Review Exercises 28. Hanging Sculpture A hanging sculpture is to be hung in an art gallery with two wires of lengths 15.0 ft and 12.2 ft so that the angle between them is 70.3°. How far apart should the ends of the wire be placed on the ceiling? 29. Height of a Tree A hill makes an angle of 14.3° with the horizontal. From the base of the hill, the angle of elevation to the top of a tree on top of the hill is 27.2°. The distance along the hill from the base to the tree is 212 ft. Find the height of the tree. 30. Pipeline Position A pipeline is to run between points A and B, which are separated by a protected wetlands area. To avoid the wetlands, the pipe will run from point A to C and then to B. The distances involved are AB = 150 km, AC = 102 km, and BC = 135 km. What angle should be used at point C? 31. Distance between Two Boats Two boats leave a dock together. Each travels in a straight line. The angle between their courses measures 54° 10′. One boat travels 36.2 km per hr, and the other travels 45.6 km per hr. How far apart will they be after 3 hr? 32. Distance from a Ship to a Lighthouse A ship sailing parallel to shore sights a lighthouse at an angle of 30° from its direction of travel. After the ship travels 2.0 mi farther, the angle has increased to 55°. At that time, how far is the ship from the lighthouse? 308 558 2.0 mi 33. Area of a Triangle Find the area of the triangle shown in the figure using Heron’s area formula. x y (–8, 6) (3, 4) (0, 0) 34. Show that the triangle in Exercise 33 is a right triangle. Then use the formula = 1 2 ac sin B, with B = 90°, to find the area. 70.3° 15.0 ft 12.2 ft 548 109
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