SOLUTION: A boy stands at a point M on the same horizontal level as the foot, T, of a vertical building. He observes an object on the top, P of the building at an angle of elevation of 66°.

Algebra ->  Trigonometry-basics -> SOLUTION: A boy stands at a point M on the same horizontal level as the foot, T, of a vertical building. He observes an object on the top, P of the building at an angle of elevation of 66°.      Log On


   

Question 1203002: A boy stands at a point M on the same horizontal level as the foot, T, of a vertical building. He observes an object on the top, P of the building at an angle of elevation of 66°. He moves directly backwards to a new point C and observes the same object at an angle of elevation of 53°. If |MT|=50m, :
(a)illustrate the information in a diagram;
(b)calculate, correct to one decimal place:
(i) the height of the building:
(ii) |MC|
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Assume that boy has negligible tallmess?

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

This is one way to draw the diagram

I'll let you handle the other parts.

Hints:
  • tan(angle) = opposite/adjacent
  • tan(angle PCT) = PT/CT which leads to tan(53) = h/(x+50), where x = MC and h = PT = height of the building.
  • tan(angle PMT) = PT/MT leads to tan(66) = h/50.
  • Solve that second equation for h to then plug into the other tangent equation (so you can solve for x).