Question

A hot air balloon is 100 feet straight above where it is planning to land. Sarah is driving to meet the balloon when it lands. If the angle of elevation to the balloon is 35°, how far If the away is Sarah from where the balloon will land?

Answer 1

Ground distance `~~142.81" feet to 2 decimal places"`

Explanation:

`tan(theta) =("opposite")/("adjacent")->tan(35^o)=("height")/("distance away")`

Let distance away be `d`
Let height be `h = 100" feet"`

So `color(brown)(tan(35^o)=h/d)`

We need to determine `d`

Turn everything upside down

`color(brown)(1/(tan(35^o))= d/h)`

Multiply both sides of the equation by `color(blue)(h)`

`color(brown)(color(blue)(h xx)1/(tan(35^o))= d/h color(blue)(xx h)`

`color(brown)(color(blue)(h)/(tan(35^o))= d xxcolor(blue)( h)/color(brown)(h)`

But `h/h=1`

`=> "distance "(d) =100/tan(35^o)`

`~~142.81" feet to 2 decimal places"`