SOLUTION: A guy wire of length 50 feet is attached to the ground and to the top of an antenna. The height of the antenna is 10 feet larger than the distance from the base of the antenna to

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Question 42890This question is from textbook
: A guy wire of length 50 feet is attached to the ground and to the top of an antenna. The height of the antenna is 10 feet larger than the distance from the base of the antenna to the point where the guy wire is attached to the ground. What is the height of the antenna? This question is from textbook

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!


Considering triangle ABC, So we can apply Pythagorus theorem: Hypotanuse%5E2+=+Base%5E2+%2B+Height%5E2

Here base = BC, height = AB and hypotanuse = AC.

Given: AC = 50 ft.
Let BC = x feet.
Then, AB = (x+10) feet
[This is because height of the antenna is 10 ft larger than the distance from the base of the antenna to the point where the guy wire is attached to the ground].

So from Pythagorus theorem we have
50%5E2+=+x%5E2+%2B+%28x%2B10%29%5E2
or 50%5E2+=+x%5E2+%2B+x%5E2+%2B+20x+%2B+10%5E2
or 2x%5E2+%2B+20x+%2B+10%5E2+-+50%5E2+=+0
or 2x%5E2+%2B+20x+%2B+100+-+2500+=+0
or 2x%5E2+%2B+20x+-+2400+=+0
or x%5E2+%2B+10x+-+1200+=+0
or x%5E2+%2B+40x+-+30x+-+1200+=+0
or x%28x+%2B+40%29+-+30%28x+%2B+40%29+=+0
or %28x%2B40%29%28x-30%29=0

So either (x + 40) = 0 or (x - 30) = 0 i.e. either x = -40 or x = 30.
Now, 'x' being the length of a side of a triangle cannot be negative.

So x = 30 i.e. the distance of the base of the antenna from the point where the guy wire is attached to the ground is 30 feet.

Hence, the height of the antenna is (x+10) = 30+10 = 40 feet.