a post is 20 m high. the angle of elevation of top of a house which is in front of the post is 30° from its top and 45° from foot . Find the height of house and distance between them.
Draw a diagram, as usual. If the post is x meters from the house, which has height h,
h/x = tan 45° = 1
So, h = x
(h-20)/x = tan 30° = 1/√3
But, h=x, so
(h-20)/h = 1/√3
h-20 = h/√3
(1-1/√3)h = 20
h = 20/(1-1/√3) = 47.32 m