Question

He bell tower of the cathedral in pisa, italy, leans 5.6 from the vertical. a tourist stands 105 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 29.2. find the length of the tower to the nearest meter.

Answer 1

we know that

see the attached figure to better understand the problem

the sinus law establishes
a/sin A=b/sin B=c/sin C

in this problem
a=105 m
A=66.4°
b=AB (length of the tower)
B=29.2°

then
a/sin A=b/sin B-----------> b=a*sin B/sin A-------> 105*sin 29.2°/sin 66.4°
b=55.90 m

the answer is 
the length of the tower is 56 m

Answer 2

The length of the tower is calculated as 55.9m

Data;

• distance of tourist from the bell = 105m
• angle of elevation from the tourist = 29.2 degree
• angle of depression of the bell = 5.6 degree
• Length of the tower = ?

The angle the top of the tower makes with the tourist can be calculated as

$180 = 90+29.2 + x\\sum of angles in a triangle = 180\\x = 180-119.2\\x = 60.8^0\\\\x + 5.6 = 66.4^0 (actual angle)$

Sine Rule

Using sine rule, we can find the length of the tower

given that

$\frac{a}{sinA} = \frac{b}{sinB}$

Let's plug in the values and solve for the height of the tower.

$\frac{105}{sin66.4} = \frac{b}{sin29.2}\\ b = \frac{105sin29.2}{sin66.4}\\ b = 55.9m$

The length of the tower is calculated as 55.9m

Learn more on sine rule here;

https://brainly.com/question/4372174