# Thread: Trigonometry - modelling and problem solving

1. ## Trigonometry - modelling and problem solving

From the top of a cliff 160m high 2 bouys are observed. Their bearings are 337 and 308 degrees. Their respective angles of depression are 3 and 5 degrees. Calculate the distance between the buoys. I am struggling to draw the diagrams required,

2. ## Re: Trigonometry - modelling and problem solving

Picture (draw) the cliff face as a vertical line with length 160.
Radiate two vertical triangles away from this, one to each buoy, (so that the triangles are not in the same vertical plane, picture the vertical line as a hinge).
One triangle will have base angles of 5 and 90 degrees, while the other will have base angles 3 and 90 degrees.
Horizontally, the angle between the two triangles will be the difference between the two bearings.
The distance of each buoy from the base of the cliff can be calculated from the two vertical triangles, and then the distance between them using the cosine rule in the horizontal triangle, (made up by line between the two buoys and the lines between each of them and the base of the vertical line/cliff face).

4. ## Re: Trigonometry - modelling and problem solving

Thank you. I get an answer of 1595m is this correct??