Question

He original height of the leaning tower of pisa was 184 feet. at a distance of 140 feet from the base of the tower, the angle of elevation from the ground to the top of the tower is . how far is the tower leaning from the original vertical position?

Answer 1

Answer:

37.3°

Explanation:

The angle of elevation can be found by using trigonometric tan function.

$tan \theta = \frac {perpendicular}{base}$

perpendicular is given by the height of the tower = 184 ft

base = distance from the tower = 140 ft

Thus, angle of elevation:

$\theta = tan^{-1}(\frac{184}{140})=tan^{-1}{1.31}\\ \Rightarrow \theta = 52.7^o$

Now, the angle of elevation + angle made by tower from the original vertical position towards the ground = 180 -90

⇒Ф= 90° - 52.7° = 37.3°

Answer 2

Ans:; 

Let AB be the height of the leaning tower= 184 feet

Let AC be the distance from the base of the tower= 140 feet

Angle between BC and AC = 59 degrees

Applying the sine rule

AB/(Sin 59) = 140/(Sin B)

On cross multiplication we get, check image,