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?

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 60^{o} (from horizontal) and turns laterally 360^{o}.

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:

` *`

/|\

/ | \

/ | \

/ |30^{o}\

/ | \

/ 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.

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

Re: Help With word Problem

thanks for both comments, you guys made it easy