# 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.

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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.**

If the horizontal is measured from the top of the 8 foot pole and extends to the 10 foot pole, a right triangle will be formed where the distance between the poles is the horizontal and the side opposite of the twenty five degree angle is 2 feet.

We can then use trigonometry to solve for the distance (D). We know that the angle is 25 degrees, and that the side opposite of this angle is two feet. Side D is the adjacent side. Therefore, we will use tan= opposite/ adjacent to solve this problem.

Tan 25= 2 feet/ D

We multiply both sides by D to get: D(Tan 25)= 2 feet.

Then divide both sides by Tan 25: D= 2 feet/ Tan 25

Then simplify by dividing to obtain the answer:** 4.29 meters**