Question

9. Rama is using a hand glider to fly directly from the top of one cliff onto another cliff below. The glider is guided by a cable. The cliffs are 740 feet apart and the first cliff is 280 feet taller than the second cliff. How long is the cable between the cliffs?

Answer 1

791.2 ft

Explanation:

The cable is inclined and this acts as the hypotenuse. Since the other two sides are given.

`H=\sqrt {x^(2)+y^(2)}`

where x and y represent the distance between two cliffs apart and difference in heights. Substituting 740 for x and 280 for y then

`H=\sqrt {740^(2)+280^(2)}=791.20161779409930627669981858168023442712 ft\approx 791.2 ft`

Answer 2

791.2 ft to the nearest tenth.

Explanation:

From the diagram,we assume :

AD to be the height of the first cliff

BC to be the height of the second cliff

DC to be the length of the cable between the top of the two cliff.

AD=740 ft.

DE= 280 ft.

Using Pythagorean Theorem, we obtain.;

`{DE}^(2)+ {CE}^(2) = {DC}^(2)`

By substitution we obtain

`{280}^(2) + {740}^(2) =`

`\implies78400 + 547600 = {DC}^(2)`

`\implies626000= {DC}^(2)`

Taking positive square root.

`\implies DC = √(626000)`

`\implies DC =791.202 ft`