[Madihakazi]

There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angles of depression of the top and the foot of the other pole are 30 degrees and 60 degrees respectively. Find the width of the river and the height of the other pole.

[ebaines]

I'll get you started, but you should finish the problem on your own. You have two equation in two unknowns. Set up the equations using x as the height of the 2nd pole and R as the width of the river, and from the fact that the angle from the top of the first pole to the foot of the other is 60 degrees you know that:



That's one equation. Can you set up the other equation, using the fact the difference in heights (60-x) has an angle of 30 degrees across the river? Try and solve for x and R, and post back with your answer.


**EDIT**
Actually, it would be easier to note that the angle from the foot of the 2nd pole to the top of the 1st pole is 60 degrees, and since the height of the first pole is 60m, you have:



You can now solve for R. Then use that value for R in the second equation that I spoke about above.