# Help With word Problem

• Jan 26th 2013, 04:15 PM
bossmann
Help With word Problem
A student is in a stationary hot-air balloon that is momentarily fixed at 1,325 ft above a piece of land. This pilot looks down 60o (from horizontal) and turns laterally 360o

a) How many acres of land are contained by the cone created by her line of site?
b) How high would the balloon be if, using the same procedure, an area four times greater is encompassed?
• Jan 26th 2013, 07:04 PM
chiro
Re: Help With word Problem
Hey bossmann.

Hint: How do you find the radius of the circle using Pythagoras' Theorem and the sin/cos/tan relationship with a right angled triangle?
• Jan 26th 2013, 07:23 PM
Soroban
Re: Help With word Problem
Hello, bossmann!

Quote:

A student is in a stationary hot-air balloon that is momentarily fixed at 1,325 ft above a piece of land.
The pilot looks down 60o (from horizontal) and turns laterally 360o.

a) How many acres of land are contained by the cone created by her line of site?

Looking down, she will see a circle of radius $r.$
Code:

*
/|\
/ | \
/  |  \
/  |30o\
/    |    \
/ 1325|    \
/      |      \
/      |      \
/        |        \
*---------+---------*
r        r

We have: . $\tan30^o \:=\:\frac{r}{1325} \quad\Rightarrow\quad r \:=\:1325\tan30^o \:=\:764.9891067 \:\approx\:765\text{ ft.}$

The area is: . $\pi r^2 \:=\:\pi(765^2) \:=\:1,\!838,\!538.561\text{ ft}^2.$

I'll let you convert it to acres.

Quote:

b) How high would the balloon be if, using the same procedure, an area 4 times greater is encompassed?

To have four times the area, we must have twice the radius.
Therefore, the height must be twice as high: . $2 \times 1325 \:=\:2650\text{ ft.}$
• Jan 27th 2013, 11:08 AM
bossmann
Re: Help With word Problem