SOLUTION: the triangular-shaped patio has sides 23ft, 17ft, and 26ft. Find the number of square feet of surface area to be covered with concrete?

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Question 869828: the triangular-shaped patio has sides 23ft, 17ft, and 26ft. Find the number of square feet of surface area to be covered with concrete?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Draw a triangle; mine goes like this:
Base of 26, left side is 17, right side is 23. The altitude runs from the top vertex, meeting perpendicularly to the 26 length base. Angle measure t is the intersection at the left for he 17 and the 26 lengths sides.

Law Of Cosines gives, 17%5E2%2B26%5E2-2%2A17%2A26%2Acos%28t%29=23%5E2
.
skipping the steps,
highlight_green%28cos%28t%29=109%2F221%29.

Pythagorean Identity,
sin%5E2%28t%29=1-cos%5E2%28t%29
. simplification steps
sin%28t%29=sqrt%281-%28109%2F221%29%5E2%29
. more simplifications,
highlight_green%28sin%28t%29=%284%2F221%29sqrt%282310%29%29

AREA was wanted.
A for Area.
A=%281%2F2%29%28base%29%28altitude%29, where "altitude" is the height.
The altitude is 17%2Asin%28t%29, and we now found sin(t).
-
highlight_green%28A=%281%2F2%2926%2A17%2A%284%2F221%29sqrt%282310%29%29
A=13%281%2F13%29%2A4sqrt%282310%29
highlight%28A=4sqrt%282310%29%29