Trigonometry - Leaning Tower of Pisa question.?
The Leaning Tower of Pisa, which was the belltower of the Cathedral in Pisa, was 184.5 feet tall when it was built perpendicular to the ground in 1173. At a distance of 123 feet from the base of the tower, the angle of elevation to the top is measured as 60degrees. What is the angle that the tower is leaning and what is the perpendicular height of the tower today?
- SeanLv 51 decade agoFavorite Answer
I am assuming that the angle measuring device, the centre of the top of the tower and the center of the base of the tower are all in the same plane.
I am also assuming that the measuring device is on the side of the tower which leans towards that measuring device.
Consider the triangle ABC such that A is the position of the angle measuring device, C is the center of the base of the tower and B is the center of the top of the tower.
Lines are denoted as lower case opposite angles and the
length of the tower is 'a' and equals 184.5ft.
The distance of the measuring device from the base of the tower is 'b' and equals 123ft.
We need to find the angle that the tower makes with the line of sight of the angle measuring device - call it 'B'.
Using the Sine Rule we can say
a/sinA = b/sinB
184.5/sin(60deg) = 123/sin(B)
sin(B) = [123*sin(60deg)]/184.5 = 0.57735
B = arcsine(0.57735) = 35.264deg
The angle at the base of the tower is given by
C = 180 - 60 - 35.264 = 84.736deg which means that the tower is 90 - 84.736 = 5.264deg off the vertical.
The perpendicular height of the tower is given by
184.5*cos(5.264deg) = 183.72ft.
- tipperyLv 43 years ago
ok, this may well be extra handy with a diagram, yet i will attempt my superb... Cos Ratio: 14/182 turn that right into a fragment, and locate the Cos^-a million and there is your answer! in case you could desire to entice a diagram, the biggest's 14 ft, and it varieties a precise perspective with an unlabelled line. The final line is the Tower, and hence 182 ft. Then placed an "x" interior the corner between the Tower and the floor wish I helped c: