Question

The angle of depression of the top and the bottom of a 10m tall building

Answer 1

In triangle ABD
Tan 45 degree= BD / AB
1= 10+x / AB
AB= 10+x m
therefore, ED = 10+x m
In triangle ECD
Tan 30 degree =CD / ED
1 / root 3 = x / 10+x
10+x = root 3x
10= root 3x-x
10= x(root3-1)
x = 10 / root3-1
x = 10 / root3-1 * root3+1 / root3+1 [rationalising root3-1]
= 10(root3+1) / (root3)^2- (1)^2
= 10(root3+1) / 3-1
= 10(root3+1) / 2
= 5(root3+1)
= 5(1.73+1)
= 5*2.73
x = 13.65 m

height of tower = BD = 10+x
= 10+13.65
= 23.65 m

distance between building and tower = AB = 10+x
= 10+13.65
= 23.65 m