Question

The bell tower of the cathedral in Pisa, Italy, leans 5.6° from the vertical. A tourist stands 107 m from its base, with the tower leaning directly toward her. She measures the angle of elevation to the top of the tower to be 28.6°. Find the length of the tower to the nearest meter. m

Answer 1

`l=56m`

Explanation:

From the question we are told that:

Angle from vertical
`\theta =5.6`

Horizontal Distance
`d=107m`

Angle of elevation
`\gamma=28.6`

Generally the Trigonometric equation for exterior angles is mathematically given by

`Exterior\ angles=\sum of\ two\ interior\ angles`

Where

`Exterior angles=90 \textdegree +5.6 \textdegree`

Therefore

`90 \textdegree +\theta \textdegree=\omega+\gamma`

`90 \textdegree +5.6 \textdegree=\omega+28.6 \textdegree`

`\omega=67 \textdegree`

Generally the equation for The Sine rule is mathematically given by

`(sin \omega )/(d)=(sin \gamma)/(l)`

`l=(107 sin 28.6)/(sin 67 \textdegree )`

`l=56m`