Hi, I would appreciate any help with the problem below.
A river flows due east and a tower [cd] stands on its left-hand bank. From a point a upstream and on the same bank of the river, the angle of elevation of the top of the tower is 60 degrees. From point b at right angles across the river from a, the angle of elevation is 45 degrees. If the height of the tower is 36 metres, find the width of the river, correct to the nearest metre.
Textbook answer is 29 metres.
Workings: there is a right triangle acd on the left-hand bank. [ad] is 21 metres which I got from the tan of 60 degrees. [ac] is 42 metres. This is where I am stuck. I have been trying to look for a second right angle triangle where I can use side [ad] and one other angle to calculate the river's width. Also, from my reading of the question I cannot see how the angle of elevation of the top of the tower from b is just 45 degrees. I know that this is an error on my part, but I just can't see it. I have looked at congruent angles for pointers.
Apologies for not attaching a drawing due to the risk of computer viruses. I hope that I am making some sense and I would appreciate any pointers / tips.