SOLUTION: a boat is 80 feet from the base of cliff. if the distance from the top of the cliff to the boat is 20 less than twice the height of the cliff to the water. Find the height of the c

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: a boat is 80 feet from the base of cliff. if the distance from the top of the cliff to the boat is 20 less than twice the height of the cliff to the water. Find the height of the c      Log On

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Question 1093199: a boat is 80 feet from the base of cliff. if the distance from the top of the cliff to the boat is 20 less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest tenth of a foot if necessary.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h+ = height of cliff in feet
given:
+2h+-+20+ = distance of boat to top of cliff
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+80%5E2+%2B+h%5E2+=+%28+2h+-+20+%29%5E2+
+6400+%2B+h%5E2+=+4h%5E2+-+80h+%2B+400+
+3h%5E2+-+80h+-6000+=+0+
Use quadratic formula
+h+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+3+
+b+=+-80+
+c+=+-6000+
+h+=+%28-%28-80%29+%2B-+sqrt%28+%28-80%29%5E2-4%2A3%2A%28-6000%29+%29%29%2F%282%2A3%29+
+h+=+%28+80+%2B-+sqrt%28+6400+%2B+72000+%29%29%2F6+
+h+=+%28+80+%2B+sqrt%28+78400+%29+%29%2F6+
+h+=+%28+80+%2B+280+%29+%2F+6+
+h+=+360%2F6+
+h+=+60+
The cliff is 60 ft high
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check:
+80%5E2+%2B+h%5E2+=+%28+2h+-+20+%29%5E2+
+80%5E2+%2B+60%5E2+=+%28+2%2A60+-+20+%29%5E2+
+6400+%2B+3600+=+100%5E2+
+10000+=+10000+
OK