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:
x ≈ 32,635 ft
Thus, the distance between two towns is 32,635 ft.
Answer:
32635.17 ft
Explanation:
In the diagram, AB = 25000 ft
Let C and D be the town, where CD = d (Distance between two towns)
By triangle, ABC
tan 50 = AB / AC
AC = 25000 / tan 50 = 20977.5 ft
By triangle, ABD
tan 25 = AB/AD
AD = 25000 / tan 25 = 53612.67 ft
So, the distance between two towns
d = AD - AC = 53612.67 - 20977.5 = 32635.17 ft
Thus, the distance between two towns is 32635.17 ft.
