Answer:
The towns are 32,635 ft apart.
Explanation:
From the image drawn below:
AB = x ft
BC = a ft
AC = (x + a) ft
Considering triangle PCB,
tan 50° = 25000 / a
Or,
a = 25000 / tan 50°
Since tan x = 1/ cot x
a = 25000×cot 50°------------------------------------1
Considering triangle PCA,
tan 25° = 25000 / (a + x)
Or,
a + x = 25000 / tan 25°
Since tan x = 1/ cot x
a + x = 25000×cot 25° -------------------------------2
Thus, finding x from equation 1 and 2, we get:
x = 25000 (cot 25° - cot 50°)
Using cot 25° = 2.1445 and cot 50° = 0.8394, we get:
<u>x ≈ 32,635 ft</u>
<u>Thus, the distance between two towns is 32,635 ft.</u>
