A room in the shape of a triangle has sides of length 7 yd, 8 yd, and 11 yd. If carpeting costs $17.50 a square yard and padding costs $3.25 a square yard, how much to the nearest dollar will it cost to carpet the room, assuming that there is no waste?

770 dollars I think I'm not 100% sure

3. By sketching this triangle it can be determined that this is not a right triangle, but rather an oblique-angled triangle. For the lengths of the three sides, let a = 7, b = 8, and c = 11, and let angle A be opposite side a, and angle B be opposite side b, and angle C be opposite side c.

Using the Law of Cosines:

cos (A) = (b² + c² - a²) / 2bc = [ (8) ² + (11) ² - (7) ²) / 2 (8) (11) = 0.773

A = acos (0.773) = 39.4°

Using the Law of Sines:

sin (A) / a = sin (B) / b = = > sin (B) = (b/a) sin (A) = (8/7) sin (39.4°) = 0.725

B = asin (0.725) = 46.5°

Knowing angles A and B, angle C is:

C = 180° - A - B = 180° - 39.4° - 46.5° = 94.1°

Finally, the area is:

Area = (ab/2) sin (C) = [ (7) (8) / 2]sin (94.1°) = 27.928 yd²

The total cost is (27.928) ($17.50 + $3.25) = $579.51 [answer (a) ]