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?
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?
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.
Yes, you are correct. The Pythagorean theorem can be used to solve this problem.
Let's label the height (or the vertical distance from the base of the stem to the break) as 'h'. Also, since the tip of the stem touches the ground 3 ft from the base, we can label the distance from the base to the tip as 'a', and the distance from the tip to the break as 'b'.
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, we can set up the equation as follows:
a^2 + h^2 = (a + b)^2
Simplifying the equation, we have:
a^2 + h^2 = a^2 + 2ab + b^2
Now, let's substitute the given values into the equation:
a = 3 ft
b = 10 ft (total length of the bamboo stem)
a^2 + h^2 = (3^2) + 2(3)(10) + 10^2
Simplifying further,
9 + h^2 = 9 + 60 + 100
h^2 = 169
h = sqrt(169)
h = 13 ft
Therefore, the height of the break is 13 ft.
Yes, you are correct! The Pythagorean theorem can be used to solve this problem. Here's how you can use it to find the height of the break:
Step 1: Visualize the problem
To better understand the situation, picture a right-angled triangle formed by the broken bamboo stem and the distance it touches the ground. The base of the triangle is the distance between the base of the stem and the point where it touches the ground (3 ft). The hypotenuse of the triangle is the length of the bamboo stem (10 ft). The height of the break is the unknown side we are trying to find.
Step 2: Apply the Pythagorean theorem
According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the length of the bamboo stem (10 ft), and one of the sides is the base of the triangle (3 ft). Let's call the height of the break "h".
Using the Pythagorean theorem, we can write the equation:
(3 ft)^2 + h^2 = (10 ft)^2
Step 3: Solve the equation
Simplifying the equation, we have:
9 + h^2 = 100
Subtracting 9 from both sides, we get:
h^2 = 91
To find the value of "h", we take the square root of both sides:
h = √91
Step 4: Calculate the height of the break
Using a calculator, we find that the square root of 91 is approximately 9.54 ft.
Therefore, the height of the break in the bamboo stem is approximately 9.54 ft.
Remember to round your answer appropriately based on the level of accuracy needed in your final exam.
I hope this helps! Let me know if you have any further questions.
(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