Question

Austin's eye-level height is 120 ft above sea level, and Anna's eye level height is 270 ft above sea level. How much further can Anna see to the horizon?

Answer 1

Answer:

C

Step-by-step explanation:

$Austin = \sqrt{ \frac{3h}{2} } \\ \\ Austin = \sqrt{ \frac{3(120)}{2} } \\ \\ Austin = \sqrt{3(60)} \\ \\ Austin = \sqrt{180} \\ \\ Austin = 6 \sqrt{5}$

$Ana = \sqrt{ \frac{3h}{2} } \\ \\ Ana = \sqrt{ \frac{ 3(270)}{2} } \\ \\ Ana = \sqrt{ 3(135) } \\ \\ Ana = \sqrt{405} \\ Ana = 9 \sqrt{5}$

How much further can Anna see to the horizon?

$Ana - Austin = 9 \sqrt{5} - 6 \sqrt{5} \\ Ana - Austin = 3 \sqrt{5}$

Answer 2

Anna can see $3\sqrt{5}$ miles further. So, the third option is correct.

It is given that,

• Austin's eye-level height is 120 ft above sea level.
• Anna's eye-level height is 270 ft above sea level.

Explanation:

Formula used:

$d=\sqrt{\dfrac{3h}{2}}$

where, $d$ is the distance they can see and $h$ is the eye-level height.

The distance Austin can see is:

$d_1=\sqrt{\dfrac{3(120)}{2}}$

$d_1=\sqrt{180}$

$d_1=6\sqrt{5}$

The distance Anna can see is:

$d_2=\sqrt{\dfrac{3(270)}{2}}$

$d_2=\sqrt{405}$

$d_2=9\sqrt{5}$

The difference in the distance they can see is:

$d=d_2-d_1$

$d=9\sqrt{5}-6\sqrt{5}$

$d=3\sqrt{5}$

Thus, the third option is correct.

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