<PRE><B>Question 166988</B>
The mainsail of a Lightning sailboat is a right triangle in which the hypotenuse is called the leech. If a 24-ft tall mainsail has a leech length of 26 ft and if sailcloth costs $10 per square foot, find the cost of a new mainsail.
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Let x = base of right triangle
then applying Pythagorean theorem:
x^2 + 24^2 = 26^2
x^2 + 576 = 676
x^2 = 100
x = {-10, +10}
.
We can toss out the negative solution leaving us with
base = 10 ft
.
Area of sail = (1/2)bh
Area of sail = (1/2)(10)(24)
Area of sail = (5)(24)
Area of sail = 120 sq ft
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Finally, if it is $10 per sq ft:
10 * 120 = $1200 (cost of new mainsail)



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