SOLUTION: A woman is planning a patio. the triangular-shaped patio has sides 25 ft, 23 ft, and 30 ft. I need to find the number of square feet of surface area to be covered with concrete.

Algebra ->  Surface-area -> SOLUTION: A woman is planning a patio. the triangular-shaped patio has sides 25 ft, 23 ft, and 30 ft. I need to find the number of square feet of surface area to be covered with concrete.       Log On


   

Question 864804: A woman is planning a patio. the triangular-shaped patio has sides 25 ft, 23 ft, and 30 ft. I need to find the number of square feet of surface area to be covered with concrete.
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This is not a right triangle because 25%5E2%2B23%5E2=1154%3C%3E900.

Let q = measure of angle for vertex of the 23 ft. side with the 30 ft. side.
The 25 ft. side is opposite of angle with measure q.

Law of Cosines
23%5E2%2B30%5E2-2%2A23%2A30%2Acos%28q%29=25%5E2
-2%2A23%2A30%2Acos%28q%29=25%5E2-23%5E2-30%5E2
cos%28q%29=%2820%5E2%2B23%5E2-25%5E2%29%2F%282%2A23%2A30%29
cos%28q%29=304%2F%282%2A23%2A30%29
152%2F%2823%2A30%29
76%2F%2823%2A15%29
highlight_green%28cos%28q%29=76%2F345%29----something seems not right about this---
highlight_green%28q=77.2739%29 degrees.

The height of this triangle, using base of 30 feet, is 23%2Asin%2877.2739%29.
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Area, highlight%28highlight%28A=%281%2F2%2930%2A23%2Asin%2877.2739%29%29%29, which you need to simplify, and you will want to round to the nearest square foot, or maybe to the nearest tenth of a square foot.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
12 sqrt(546)=280.4 sq ft