Assume that a surveyor stands at the top of a mountain that is "h" feet tall. if the distance (in feet) that he can see is defined by d = 3200.2 sqrt(h), then answer the following. (a) how far can the surveyor see from the top of a 2000-foot mountain? (b) how tall is the mountain, if the surveyor can see 15 miles? (note: 1 mile equals 5280 feet.)

a) d = 143,117 ft

b) h = 612.45 ft

Step-by-step explanation:

If height of the mountain = h  

And distance till the surveyor can see = d = 3200.2 SQRT (h)

Refer to attached file for graphical representation

Then;

A)If h=2000 ft

Then d =3200.2 √ (2000)

d = 3200.2 (44.72)

d = 143,117 ft

B)If d = 15 miles

1mile = 5280 ft

15 mile = 15*5280

15 mile = 79,200 ft

Therefore;

d = 79,200 ft

Since,

d =3200.2 √ (h)  

79,200 = 3200.2 √ (h)

79200/3200.2 =√ (h)

√ (h) = 24.75

{√ (h)} ² = (24.75) ²

h = 612.45 ft