Calculate the height of the pinnacle.

Question

A metal structure forms the pinnacle of a church tower built of face bricks .The brick section is 43,42 m high.The angle of elevation from a point on the ground to the top of the pinnacle is 40degrees 15 minutes and to the bottom of the pinnacle ,the angle of elevation is 36 degrees 10 minutes

Answer 1

The picture diagrammatically shows the problem. The point on the ground from which the elevations are measured is X on the diagram and the line XT to the bottom of the pinnacle TP is at an angle 36º10' to the ground. The line XP is at an angle 40º15' to the ground (the angle is shown for legibility as 90-40º15'=49º45' (49.75º) at the top of the diagram). The distance of X from the base of the tower is given by (height of the tower)*cot(36º10')=43.42*1.368=59.3984m. The height of P, the top of the pinnacle, is 59.3984*tan(40º15')=50.2844m, making the height TP of the pinnacle structure 50.2844-43.42=6.8644m.