A forest fire is spotted from two fire towers.
The triangle formed by the two towers and the fire
has angles of 29° at tower A and 37° at tower B. If
the towers are 3000 meters apart, how far is each
tower from the fire?

11,346 m and 8,346 m

Step-by-step explanation:

The situation is represented in the figure attached. We have:

- O is the position of the fire

- A' is the position of tower A on the ground

- B' is the position of tower B on the ground

is the angle formed by the triangle AOA'

is the angle formed by the triangle BOB'

The distance between A' and B' is A'B' = 3000 m

Using trigonometry, we have the following relationships:

They can be rewritten as

We also know that

Substittuing the two previous equations into this ,we get

Assuming that the two towers are identical, they have same height, so

And we can solve the equation to find the height of the towers:

And so, the distance of each tower from the fire is:

c.

step-by-step explanation:

she should of added 9^2 and 12^2. that is because it is a^2+b^2=c^2. c^2 is the hypotenuse and should always be bigger than the other two numbers. which is why she should of added 9 squared and 12 squared together instead of 15 squared.