Question

Diagram: http://img366.imageshack.us/img366/8884/trigoquestion1ek4.jpg

A man, M, positions himself on a river bank, as in the diagram alongside, so he can observe two poles A and B of equal height on the opposite bank of a river.

He finds the angle of elevation to the top of A is 22 degrees, and the angle of elevation to the top of B is 19 degrees. Show how he could use these facts to determine the width of the river, given that A and B are 100m apart.

Answer 1

let the height of the two towers be y and x be the width of the river.
according to the information given and the diagram, tan22=y/x and tan19=y/(100^2+x^2)^1/2. The denominator is obtained through Pythagoras Theorem

By making y the subject of both equations and equating the two together, the equation would look something like xtan22=tan19(100000+x^2)^1/2.

x(tan22/tan19)=(100000+x^2)^1/2
1.17x=(100000+x^2)^1/2.
1.38x^2=100000+x^2
0.38x^2=10000
x=162.9 (1 d.p)