# Thread: Base from height, and ?

1. ## Base from height, and ?

From the top of a fire tower (100 M), two fires are seen at opposite points. (i.e., north and south) The angle of depression to one fire is 5 degrees, and 6 degrees to the other. What is the distance between the two fires (length of the base of the triangle) ?

2. Originally Posted by zoso
From the top of a fire tower (100 M), two fires are seen at opposite points. (i.e., north and south) The angle of depression to one fire is 5 degrees, and 6 degrees to the other. What is the distance between the two fires (length of the base of the triangle) ?
some info is missing, are the fires at ground level?

3. Originally Posted by zoso
From the top of a fire tower (100 M), two fires are seen at opposite points. (i.e., north and south) The angle of depression to one fire is 5 degrees, and 6 degrees to the other. What is the distance between the two fires (length of the base of the triangle) ?
assuming they are ground-level...

Let's concentrate on the fire with 5 degree depression, if it is going down five degrees, than the amount of degrees between the distance line and the tower is $\displaystyle 90-5=85$
so we need to find the distance between the base of the tower to the fire, to do that we use the tan of 85 and multiply by the height of the tower: $\displaystyle 100\tan85$

Now let's concentrate on the fire with 6 degree depression, if it is going down five degrees, than the amount of degrees between the distance line and the tower is $\displaystyle 90-6=84$
so we need to find the distance between the base of the tower to the fire, to do that we use the tan of 84 and multiply by the height of the tower: $\displaystyle 100\tan84$

now we add the distances together...
$\displaystyle \boxed{100\tan85+100\tan84}$

(I don't have a calculator handy, so you'll need to find those lengths)

4. Originally Posted by Quick
some info is missing, are the fires at ground level?
Yes, the fires are at ground level. The outpost is exactly 100 M above the ground.

The angles given are the angles between the horizontal plane that the outpost sits on, and the slopes descending to two opposite points, the fires.

You could try and a more step by step explanation to the distance, but I think I understand anyway.

5. No need, for further explanation actually, I'm pretty sure, I fully understand the processes involved.

The final distance works out to something like 2094 m, if I'm correct

6. Originally Posted by zoso
No need, for further explanation actually, I'm pretty sure, I fully understand the processes involved.

The final distance works out to something like 2094 m, if I'm correct
You are correct.