Answer :
Answer:
Therefore,
The height of the tree is 7 ft.
Step-by-step explanation:
Consider a diagram shown below such that
Let,
AB = h = height of tree
'C' is a point on the ground 24 ft from the base 'B' of a tree
BC = 24 ft
The distance to the top of the tree is 4 ft more than 3 times the height of the tree
AC = 4 + 3h
To Find:
AB = h = ? ( height of tree)
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}=AB^{2}+BC^{2}[/tex]
Substituting the values we get
[tex](4+3h)^{2}=h^{2}+24^{2}[/tex]
Using (A+B)²=A²+2AB+B² we get
[tex]16+24h+8h^{2}=h^{2}+24^{2}[/tex]
[tex]8h^{2}+24h-560=0[/tex]
Dividing through out by 8 we get
[tex]h^{2}+3h-70=0[/tex]
Which is a quadratic equation, so on factorizing we get
[tex](h+10)(h-7)=0\\h+10 =0\ or\ h-7 =0\\h= -10\ or\ h =7[/tex]
h cannot be negative therefore ,
[tex]h = 7\ ft[/tex]
Therefore,
The height of the tree is 7 ft.
