SOLUTION: A painter needs to cover a triangular region 65 feet by 50 feet by 60 feet.If a can of paint covers 50 square feet. What is the least number of cans that will be needed?

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Question 977351: A painter needs to cover a triangular region 65 feet by 50 feet by 60 feet.If a can of paint covers 50 square feet. What is the least number of cans that will be needed?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Make a drawn figure:
65 unit base, one side at the left 60 unit, one side at the right 50 unit;
angle at left call as alpha. That is the triangle.

Law of Cosines:
60%5E2%2B65%5E2-2%2A60%2A65%2Acos%28alpha%29=50%5E2
do the steps...
cos%28alpha%29=5325%2F7800
cos%28alpha%29=0.6826923
alpha=46.94561

You need sine of alpha.
highlight%28sin%28alpha%29=0.7307%29

AREA, %281%2F2%29%2Abase%2Aheight;
You know base but need to calculate height.
Height, 60%2Asin%28alpha%29
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Now compose area expression in number values:
Area, highlight%28%2860%2Asin%28alpha%29%2A65%29%2F2%29
Area is highlight%281424.8%2AsquareFeet%29.

How Many Paint-Cans Needed?
highlight%281424.8%2F50=highlight%2828%261%2F2%29%29

Painter will prepare with 29 whole cans, but would use estimated 28.5 of them; half a can be go unused.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A painter needs to cover a triangular region 65 feet by 50 feet by 60 feet.If a can of paint covers 50 square feet. What is the least number of cans that will be needed
Using Heron's formula, you should get an area of 1,424.877 sq ft

Number of cans: 1424.877%2F50, or 28.49753 or a MINIMUM of highlight_green%2829%29 cans are needed