Question

I have sent you a picture of the problem I’m needing help with. Thank you

Answer 1

We need to find the height of the tree. It is represented by x in the following triangle:

Using the Pythagorean Theorem, we have:

`\begin{gathered} (1+3x)^(2)=x^(2)+35^(2) \\ \\ 1+6x+9x^(2)=x^(2)+1225 \\ \\ 1+6x+9x^(2)-x^(2)-1225=0 \\ \\ 8x^(2)+6x-1224=0 \end{gathered}`

Now, using the quadratic formula, we obtain:

`\begin{gathered} x=\frac{-6\pm\sqrt[]{6^(2)-4(8)(-1224)}}{2(8)} \\ \\ x=\frac{-6\pm\sqrt[]{36+39.168}}{16} \\ \\ x=\frac{-6\pm\sqrt[]{36+39.168}}{16} \\ \\ x=\frac{-6\pm\sqrt[]{39204}}{16} \\ \\ x=(-6\pm198)/(16) \\ \\ x_1=(-6-198)/(16)=(204)/(16)=12.75 \\ \\ x_2=(-6+198)/(16)=(192)/(6)=12 \end{gathered}`

Since x is the height of the tree, it needs to be a positive value. Then, only x₂ is possible.

Therefore, the height of the tree is 12 ft.