Question

from the top of a hill the angles of depression of two consecutive km stones due east are found to be 30 degree and 45 degree find the height of the hill

Answer 1

Let the height of hill AB be x cm
And the two consecutive km stones be C and D
Distance CD = 1 km = 1000 m
In triangle ABC
tan45 = AB/BC = AB/x
1 = AB/x
x = AB

BD = BC+CD
= x+1000 m
In triangle ABD
tan30 = AB/BD
1 / √3 = x / x+1000
x+1000 = √3x
1000 = x(√3-1)
1000 / (√3-1) = x
1000(√3+1) / (√3-1)(√3+1) = x
1000(1.73+1) / √3²-1² = x
1000(2.73) / 2 = x
500×2.73 = x
x = 1365 m
So the height of hill is 1365m