Question

The leaning tower of Pisa in Italy leans at an angle of about 84°. The figure below shows 52.1 meters from the base of the tower, the angle of elevation to the top is 50°. Find the distance (b) from the base to the top of the tower.
The measure of angle C

Answer 1

the distance to the nearest foot from the base to the top of the tower is 184 feet .

Step-by-step explanation:

Here we have , The leaning tower of Pisa in Italy leans at an angle of about 84°. The figure below shows 52.1 meters from the base of the tower, the angle of elevation to the top is 50°. We need to find the distance to the nearest foot from the base to the top of the tower . Let's find out:

Let angle A = 50

Let Angle B = 84

Since the angles of a triangle must add up to 180, then

Angle C = 180-50-84 = 46

Now, use the law of sines to find the distance from the base to the top of the tower. That is the side of the triangle opposite Angle A. The distance of 52.1 feet is the side opposite Angle C. So:

⇒ $\frac{a}{sin(a)}= \frac{c}{sin(c)}$

⇒ $\frac{a}{sin(50)}= \frac{52.1}{sin(46)}$

⇒ $a= \frac{52.1}{sin(46)}(sin(50)$

⇒ $a= \frac{52.1}{0.72}(0.76)$

⇒ $a=55ft$

Therefore , the distance (b) from the base to the top of the tower is 55 feet .