Question

a balloon that is tied to a stake in the ground is being blown sideways by the wind. the length of the string from the stake to the balloon is 26 feet, and the distance from the stake to point directly under the balloon is 24 feet.
if x is the distance in feet from the balloon to the ground, what is the value of x?
25
2
4
10

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 26\) (length of the string), \(a=24\) (distance from stake to point under balloon), and \(b = x\) (distance from balloon to ground). So, \(x^{2}+24^{2}=26^{2}\).

Step2: Simplify the equation

\(x^{2}=26^{2}-24^{2}\). Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\), we have \(x^{2}=(26 + 24)(26-24)\). Then \(x^{2}=(50)\times(2)=100\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x>0\) (distance), \(x=\sqrt{100}\).

Answer:

\(10\)