The church spire will be west of the road.
The angle at the first point (call that point A)
from the road at point A to the spire is 342 degrees or
the acute angle is 360 - 342 = 18 degrees.
The angle at the second point (call that point B)
from the road at point B to the spire is 337 degrees or
the acute angle is 360 - 337 = 23 degrees.
You want to know the distance the spire is from the road.
The shortest distance or the perpendicular distance.
Let's call that distance "h"
Let's call the distance walked "d" which we know is 1500m.
The distance from point A to the perpendicular point is
1500 + unknown distance along the road.
(let's call the unknown distance "x".)
The distance from point B to the perpendicular point is
the unknown distance along the road.
Let's call the unknown distance "x"
for a right triangle:
the height of the triangle is the base times the tangent of the angle from the base to the apex of the triangle.
----> EQUATION 1
Since both equations are equal to h, they are equal to each other.
expanding the LHS
simplify the RHS
Then plug X back into equation 2 to determine the perpendicular distance the spire is west of the road -- the "h" in both equations.
plug it back into equation 1.