Solve the problem. A room in the shape of a triangle has sides of length 18.5 ya

Question

Solve the problem. A room in the shape of a triangle has sides of length 18.5 yards, 147 yards, and 20.9 yards. If carpeting costs $21.83 per square yard, padding costs $2.30 per square yard, and there is no charge for installation, how much, to the nearest dollar, will it cost to carpet the room? A triangular-shaped field has sides of 226.3 meters and 194.4 meters, and the angle between them measures 68.56 degree. Find the area of the field. A hot-air balloon is rising vertically 11 ft/sec while the wind is blowing horizontally at 5 ft/sec. Find the angle that the balloon makes with the horizontal. The sides of a parallelogram are 15 ft and 17 ft. One angle is 40 degree while another angle is 140 degree. Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot). Lookout station B is located 15 mi due east of station A. The bearing of a fire from A is S10 degree 20'W and the bearing from B is S32 degree 50'W. Determine the distance from the fire to B (to the nearest tenth of a mile). Two airplanes leave an airport at the same time, one going northwest at414 mph and the other going east at 345 mph. How far apart are the planes after 4 hours (to the nearest mile)? To find the distance AB across a river, a distance BC = 238 m is laid off on one side of the river. It is found that B = 105.1 degree and C = 15.1 degree. Find AB.

Explanation / Answer

Triangle with sides : a = 18.5 yars; b = 14.7 yard ; c = 20.9 yard

Ares of triangle = sqrt(s(s-a)(s-b)(s-c))

s = (a+b+c)/2 = 27.05

Area =sqrt(27.05*(27.05 -18.5)(27.05 -14.7)(27.05 -20.9))

= 132.54 sqyard

Cost of carpeting = (21.83 +2.3)(132.54) = $ 3198.19

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