Question

how far you can see on a clear day depends on where you are. on the ocean or on flat land the distance (d) to the horizon in miles can be found by using the formula $d = sqrt{1.5h}$. the variable h stands for the height of your eye above the land (in feet). use the formula to answer each question. measure or estimate the height of your own eye to the nearest tenth of a foot. how far out can you see from a beach? how far away would the horizon be if you were standing on top of an 80 - foot tower? (remember to add the height of your eye to the towers height.) how far is the horizon from the top of a 2000 - foot mountain? how far could you see from a plane flying three miles up? when the area of a circle is known, the diameter (d) can be found by using the formula $d = 2sqrt{\frac{a}{3.14}}$. a small - size pizza covers about 80 square inches. what is its diameter (to the nearest tenth of an inch)? what would be the diameter of a pizza twice as large (twice as much to eat)?

Explanation:

1. Distance to the horizon from beach (assuming average eye - height of 5.5 feet)

Step1: Substitute height value

Substitute $h = 5.5$ into $d=\sqrt{1.5h}$
$d=\sqrt{1.5\times5.5}$

Step2: Calculate square - root

$d=\sqrt{8.25}\approx2.9$ miles

2. Distance to the horizon from an 80 - foot tower (assuming average eye - height of 5.5 feet)

Step1: Calculate total height

$h=80 + 5.5=85.5$ feet

Step2: Substitute into formula

$d=\sqrt{1.5\times85.5}$

Step3: Calculate square - root

$d=\sqrt{128.25}\approx11.4$ miles

3. Distance to the horizon from a 2000 - foot mountain

Step1: Substitute height value

Substitute $h = 2000$ into $d=\sqrt{1.5h}$
$d=\sqrt{1.5\times2000}$

Step2: Calculate square - root

$d=\sqrt{3000}\approx54.8$ miles

4. Distance to the horizon from a plane flying 3 miles up (since 1 mile = 5280 feet, $h = 3\times5280=15840$ feet)

Answer:

$d=\sqrt{1.5\times5.5}\approx2.9$ miles