A 10 ft. long stem of bamboo is broken in such a way that its tip touches the ground 3 ft. from the base of the stem, as shown in the figure. What is the height of the break?

Question

please show me how to do it I'm reviewing for our final exam... thanks

in solving it, is it right to use Pythagorean theorem anyway?

Answer 1

Since we're dealing with the sides of a right triangle, I'd say the first tool to try is the Pythagorean Theorem.

If the height is h, the the length of the leaning part of the bamboo is 10-h. So, you have a right triangle where

3^2+h^2 = (10-h)^2

Now just find h.

Answer 2

(10-x)^2 + (3)^2 = x^2
100-x^2 + 9 =x^2
109 = 2x^2
Therefore, x^2 = 109÷2
= 54.4
Therefore, x= root 54.4
Which equals approximately 7.37 feet