Question

Two vertical poles are 200 m apart and the height of one is double that of the other. from the middle point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary. find the heights of the poles.

Answer 1

Hey.

let the height of the poles be x and 2x and distance between them is 200.

let the elevation be m for x....so it will be 90-m for 2x pole.

so, tan m = x/100

and tan (90-m) =2x/100=x/50
so, cot m=x/50
or, 1/tan m=x/50
or, tan m = 50/x

so, x/100=50/x
or, x^2=5000
so, x = 5×10×10×5×2=50√2 m

so, height are 50√2m and 100√2 m

Thanks.

Answer 2

height of the two poles are of 1000and 2000