SOLUTION: A tree is supported by a wire anchored in the ground 15 feet from its base. the wire is 4 feet longer then the height that it reaches on the tree. find the length f the wire?

Question 503470: A tree is supported by a wire anchored in the ground 15 feet from its base. the wire is 4 feet longer then the height that it reaches on the tree. find the length f the wire?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
f = length of the wire
f = hypotenuse of a right triangle
a = base of the triangle
a = 15
b = height of the triangle
c = b+4
.
f^2 = a^2 + b^2
.
substitute
(b+4)^2 = a^2 + b^2
.
Recall a=15
.
b^2 + 8b + 16 = 225 + b^2
subtract b^2 from both sides
8b + 16 = 225
subtract 15 from both sides
8b = 209
b = 26 1/8
.
f = 30 1/8
.
Always check your answer:
f^2 = 58081/64
= 907.515625
.
a^2 = 225
b^2 = 682.515625
a^2 + b^2 = 907.515625
.
Correct.
.
Re-read the question to determine what answer is required.
What is the length of the wire?
f = 30 1/8 ft
f = 30.125 ft
.
Done
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