Question

The Tower of Pisa is well known worldwide for how it leans,

Sami visits the tower and wants to investigate how much it is leaning. He draws a diagram
showing a non-right triangle ABC.
On the diagram the angle ACB is 55º. The horizontal displacement of the tower BX = 5m.
The length of BC is 45m.
1) find the length of tower AB ​

Answer 1

The tower is approximately 57.34 meters long

Explanation:

The given parameters are;

The type of triangle formed by ΔABC = Non-right triangle

The measure of ∠ACB = 55°

The horizontal displacement of the tower, BX = 5 m

The length of BC = 45 m

Therefore, we have;

Triangle ΔABC type = Right triangle

By the tangent to an acute angle, θ, in a right triangle, we have;

`Tan(\theta) = (Opposite \, side \ length)/(Adjacent\, side \ length)`

Where θ is the 55°, we have angle, we have;

`Tan(55^(\circ)) = (XA)/(XC)`

BC = BX + XC

∴ XC = BC - BX

XC = 45 m - 5 m = 40 m

`\therefore Tan(55^(\circ)) = (XA)/(40)`

XA = 40 × tan(55°) ≈ 57.126

The type of triangle formed by ΔABX = Right triangle

According to Pythagoras theorem, AB² = XA² + BX²

∴ AB = √((40 × tan(55°))² + 5²) ≈ 57.34

The length of the tower, AB ≈ 57.34 m