Cand D are two observation posts on the same horizontal ground at the foot A of a vertical tower AB.the tower is 18m due north of D and 24m east of C.the angle of elevation of B from D is 35¡ã.calculate to three s.f the height AB,distance CD,angle of elevation from C,bearing...

Answer 1

As with all geometry problems, draw a diagram (plan).

You will find that in right triangle ABD, we know
AD=18 m
∠ADB=35°

Solve this triangle to get
mAB=AD tan(ADB)
=18tan(35°)

For right triangle CAB,
mAB (known from above)
mCA = 24m
=>
∠ACB=tan^-1(mAB/mCA)
=angle of elevation of B relative to C.

Distance CD can be found by Pythagoras theorem.