Distance from here to there

Question

The maximum distance D in kilometres that a person can see from a height h in kilometres above the ground is given by D=112√h. Find the height that would allow a person to see a distance of 84 kilometres.

Show your work

Answer 1

This problem asks you to solve for some height h given that the distance that you will see at this height of h is 84 km. Since your formula states that D = 112√h, all you would have to do is plug in your value of D and solve for h...

84 = 112√h

(84/112)=√h [divide both side by 112]

(3/4)= √h [reduce the fraction]

(9/16) = h [square both sides]

At 9/16 of a km, you can see over a distance of 84 km

Answer 2

1) Set the equation up:

D = 112√h

2) Plug in 84 for D:

84 = 112√h

3) Solve for h:

84 = 112√h

84÷112 = √h

3/4 = √h

(3/4)² = h

9/16 = h

4) Answer: You would need to be 9/16 kilometres above the ground to see a distance of 84 kilometres away from your location.