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:
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
[tex]\left ( 3h+1 \right )^{2}=h^{2}+35^{2}[/tex]
[tex]8h^{2}+6h-1224=0[/tex]
[tex]4h^{2}+3h-612=0[/tex]
[tex]h=\frac{-3\pm \sqrt{9+4\times 4\times 612}}{8}[/tex]
[tex]h=\frac{-3\pm 99}{8}[/tex]
Take positive sign
h = 12 ft
Thus, the height of tree is 12 ft.
