Question

aaliyah and sanjay are mountain climbing and want to climb up an 80 - foot vertical rock face. aaliyah goes first while sanjay stands a few steps back from the rock face. when aaliyah reaches the top, she is 89 feet away from sanjay. how far away from the rock face is sanjay standing?
square feet

Explanation:

Step1: Define right triangle sides

Let \(x\) = Sanjay's distance from the rock face (adjacent side). Aaliyah's height: \(80\) ft (opposite side). Distance between them: \(89\) ft (hypotenuse).

Step2: Apply Pythagorean theorem

$$x^2 + 80^2 = 89^2$$

Step3: Calculate squared values

$$x^2 + 6400 = 7921$$

Step4: Solve for \(x^2\)

$$x^2 = 7921 - 6400 = 1521$$

Step5: Find square root of \(x^2\)

$$x = \sqrt{1521} = 39$$

Answer:

39 feet