581 5.4 Solutions and Applications of Right Triangles 83. Distance of a Plant from a Fence In one area, the lowest angle of elevation of the sun in winter is 23° 20′. Find the minimum distance x that a plant needing full sun can be placed from a fence 4.65 ft high. 84. Distance through a Tunnel A tunnel is to be built from A to B. Both A and B are visible from C. If AC is 1.4923 mi and BC is 1.0837 mi, and if C is 90°, find the measures of angles A and B. 85. Height of a Plane above Earth Find the minimum height h above the surface of Earth so that a pilot at point A in the figure can see an object on the horizon at C, 125 mi away. Assume 4.00 * 103 mi as the radius of Earth. 125 mi C A B h NOT TO SCALE 86. Length of a Side of a Piece of Land A piece of land has the shape shown in the figure. Find the length x. x 198.4 m 528 209 308 509 87. (Modeling) Distance between Two Points A variation of the subtense bar method that surveyors use to determine larger distances d between two points P and Q is shown in the figure. The subtense bar with length b is placed between points P and Q so that the bar is centered on and perpendicular to the line of sight between P and Q. Angles a and b are measured from points P and Q, respectively. (Data from Mueller, I., and K. Ramsayer, Introduction to Surveying, Frederick Ungar Publishing Co.) b/2 b/2 P Q a b (a) Find a formula for d involving a , b , and b. (b) Use the formula from part (a) to determine d if a = 37′ 48″, b = 42′ 03″, and b = 2.000 cm. 238 209 x 4.65 ft Plant C A B Tunnel 1.4923 mi 1.0837 mi
RkJQdWJsaXNoZXIy NjM5ODQ=