Answer:
Therefore,
The distance d is 8 feet,
and the height of the tower is 15 feet.
Step-by-step explanation:
Consider a diagram shown below such that
Let,
AC = length of wire = 17 feet
BC = d = distance from the tower's base to the end of the wire.
The height of the tower is 7 feet greater than the distance d
AB = height of tower = 7 +d
To Find:
AB = ? ( height of tower)
BC = d =?
Solution:
In Right Angle Triangle ABC by Pythagoras theorem we have
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
[tex]AC^{2}=BC^{2}+AB^{2}[/tex]
Substituting the values we get
[tex]17^{2}=d^{2}+(7+d)^{2}[/tex]
Using (A+B)²=A²+2AB+B² we get
[tex]17^{2}=d^{2}+49+14d+d^{2}\\2d^{2}+14d-240=0[/tex]
Dividing through out by 2 we get
[tex]d^{2}+7d-120=0[/tex]
Which is a quadratic equation, so on factorizing we get
[tex](d-8)(d+15)=0\\d-8=0\ or\ d+15=0\\d=8\ or\ d=-15[/tex]
d cannot be negative therefore ,
[tex]d =8\ feet[/tex]
Now substitute d in AB we get
[tex]AB=7+8=15\ feet[/tex]
Therefore,
The distance d is 8 feet,
and the height of the tower is 15 feet.
