Height of a kite

Question

Grady is flying a kite on 50 ft of string. Its vertical distance from his hand is 10ft more that the horizontal distance from his hand. Assuming that the string is being held 5 ft above ground level, find its horizontal distance from Grady and its vertical distance from the ground.

Answer 1

Let x = horizontal distance 

 

Then, x + 10 = vertical distance of kite above Grady's hand

 

By the Pythagorean Theorem, x² + (x+10)² = 50²

 

So, x² + x² + 20x + 100 = 2500

 

        2x² + 20x - 2400 = 0

 

          x² + 10x - 1200 = 0

 

         (x+40)(x-30) = 0

 

         x = -40 or x = 30

 

Since x can't be negative, x = 30 ft

 

Horizontal distance = 30 ft

Vertical distance from the ground = 5 + 40 = 45 ft