At a point on the ground 24 ft from the base of a tree, the distance to the top of the tree is 4 ft more than 3 times the height of the tree. Find the height of the tree.

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

Substituting the values we get

Using (A+B)²=A²+2AB+B² we get

Dividing through out by 8 we get

Which is a quadratic equation, so on factorizing we get

h cannot be negative therefore ,

Therefore,

The height of the tree is 7 ft.

step-by-step explanation:

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