# Thread: Help With word Problem

1. ## 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?

2. ## 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?

3. ## Re: Help With word Problem

Hello, bossmann!

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 $\displaystyle r.$
Code:
                *
/|\
/ | \
/  |  \
/   |30o\
/    |    \
/ 1325|     \
/      |      \
/       |       \
/        |        \
*---------+---------*
r         r
We have: .$\displaystyle \tan30^o \:=\:\frac{r}{1325} \quad\Rightarrow\quad r \:=\:1325\tan30^o \:=\:764.9891067 \:\approx\:765\text{ ft.}$

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

I'll let you convert it to acres.

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: .$\displaystyle 2 \times 1325 \:=\:2650\text{ ft.}$