SOLUTION: After a violent storm a 34 foot mast snapped in two, and the upper part fell with the top hitting the ground 10 feet from the foot of the mast. The upper part had not completely br
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-> SOLUTION: After a violent storm a 34 foot mast snapped in two, and the upper part fell with the top hitting the ground 10 feet from the foot of the mast. The upper part had not completely br
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Question 543783: After a violent storm a 34 foot mast snapped in two, and the upper part fell with the top hitting the ground 10 feet from the foot of the mast. The upper part had not completely broken off. How much of the mast is still above the deck and what is the length of the portion that has fallen to the deck?
You can put this solution on YOUR website! After a violent storm a 34 foot mast snapped in two, and the upper part fell with the top hitting the ground 10 feet from the foot of the mast.
The upper part had not completely broken off. How much of the mast is still above the deck and what is the length of the portion that has fallen to the deck?
:
Let m = portion of the mast that remains vertical
Let d = portion of the mast that fell to the deck
:
Originally a 34' mast, therefore:
m + d = 34
d = (34-m)
:
This forms a right triangle where:
d = the hypotenuse
m = one leg
10 = the other leg
:
d^2 = m^2 + 10^2
d^2 = m^2 + 100
replace d with (34-m)
(34-m)^2 = m^2 + 100
FOIL
1156 - 68m + m^2 = m^2 + 100
Combine like terms
-68m + m^2 - M^2 = 100 - 1156
-68m = -1056
m =
m = +15.53 ft is what's left of the mast
then
d = 34 - 15.53
d = 18.47 ft fell to the deck
:
:
Check this in a calc: enter gives us 18.47
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