# A rope joining the top of two poles that are 8 m and 10 m high makes an angle 25 degrees with the horizontal. How far apart are are the two poles.

A rope joining the top of two poles that are 8 m and 10 m high makes an angle 25 degrees with the horizontal. Let the horizontal distance between the two poles be D.

Consider the line joining the top of the two poles, the horizontal line from the top of the pole that is 8 m tall and the vertical line through the pole that is 10 m tall. The three lines form a right triangle with sides D, 2 and ` sqrt(2^2 +D^2)` . As the hypotenuse makes an angle 25 degrees with the horizontal,

`tan 25 = 2/D`

`D = 2/tan 25`

=> `D ~~ 4.289` m

The two poles are approximately 4.289 m apart.