Hello, 0110kim!

I took off from an airport at an angle of 18° (nearest degree).

At a horizontal distance of 1000 m away from where I take off

there is a range of hills 300 m high.

If I maintain an angle of 18°, show whether I will clear the range.

There are a number of ways to answer this question. Code:

* B
* |
* |
* | 300
* |
* θ |
* - - - - - - - - - - - *
A 1000 C

The 300-m hill is 1000 m away.

What angle $\displaystyle \theta$ is needed to clear the hill?

We have: .$\displaystyle \tan\theta \:=\:\frac{300}{1000} \:=\:0.3$

Hence: .$\displaystyle \theta \:=\:\arctan(0.3) \:\approx\:16.699^o$

Therefore, any angle $\displaystyle \theta > 17^o$ will clear the range.

Code:

* B
* :
* :
* : h
* :
* 18° :
* - - - - - - - - - - - *
A 1000 C

The plane takes off at 18°

How high will it be 1000 m away?

We have: .$\displaystyle \tan18^o \:=\:\frac{h}{1000} \quad\Rightarrow\quad h \:=\:1000\tan18^o \:\approx\:325$

The plane will be 325 m high; it will clear the range.