Question

There is a bamboo 10 feet high, the upper end of which, being broken, reaches the ground 5 feet from the stem. find the height of the break.The height at which the break occurs is ___. (ft, ft^2, ft^3)(Type an integer or decimal rounded to the nearest hundredth)

Answer 1

Let x be the height where the bamboo breaks.

The breaking represents a right triangle, wherein x represents the legs and the base is equal to 5 feet (ground to stem braking distance). We can use the Pythagorean theorem to solve for the value of x, such that

$\begin{gathered} c^2=a^2+b^2 \\ c=\sqrt[]{x^2+5^2} \\ c=\sqrt[]{x^2+25} \end{gathered}$

The total height of the bamboo is equal to the value of x plus the value of c. Hence, we can have the equation

$\begin{gathered} x+c=10 \\ x+\sqrt[]{x^2+25}=10 \end{gathered}$

Solve for x, we get

$\begin{gathered} \sqrt[]{x^2+25}=10-x \\ x^2+25=(10-x)^2 \\ \cancel{x^2}+25=100-20x+\cancel{x^2} \\ 20x=100-25 \\ 20x=75 \\ x=\frac{75}{20} \\ x=3.75 \end{gathered}$

Therefore, the break occurs at 3.75 ft.

Answer: 3.75 ft