Two poles of heights 38 m and 56 m are connected by a cable. The cable makes an angle of 30° with the horizontal.
The height difference between the poles is:
56−38=18 m
The cable connects the top of the shorter pole to the top of the taller pole. This creates a right triangle where:
- Vertical side (opposite) = 18 m
- Horizontal side (adjacent) = d (distance between bases)
- Angle with horizontal = 30°
Using the tangent ratio:
tan(30°)=adjacentopposite=d18
Since:
tan(30°)=31:
31=d18
d=183 m