Question

At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree

Answer 1

Answer:

Step-by-step explanation:

This is a question that uses the Pythagorean Theorem.

a = 35 feet

b = x            which is the height of the tree.

c = 3*x + 1   so we are trying to find x.  Substitute into a b and c

a^2 + b^2 = c^2

35^2 + x^2 = (3x + 1)^2        

35^2 + x^2 = 9x^2 + 6x + 1     Subtract x^2 from both sides.

35^2 = 8x^2 + 6x + 1               Subtract 35^2 from both sides.

0 = 8x^2 + 6x + 1 - 35^2

0 = 8x^2 + 6x - 1224

Does this factor?

(x + 12.75)(x - 12)

x - 12 = 0 is the only value that works.

x = 12

The tree is 12 feet high.

Note: I used the quadratic formula to solve this.

Answer 2

Answer:

12 ft

Step-by-step explanation:

Let the height of the tree is h.

So the distance of top of the tree = 3 h + 1

Distance of base of tree = 35 ft

So, by use of Pythagoras theorem

$\left ( 3h+1 \right )^{2}=h^{2}+35^{2}$

$8h^{2}+6h-1224=0$

$4h^{2}+3h-612=0$

$h=\frac{-3\pm \sqrt{9+4\times 4\times 612}}{8}$

$h=\frac{-3\pm 99}{8}$

Take positive sign

h = 12 ft

Thus, the height of tree is 12 ft.