The CN Tower is 553m high. A person in a boat on Lake Ontario, at a point B due south of the tower, observes the top (T) of the tower at an angle of elevation of 8 degrees. At the same time, another person, at a point C on a bearing {S 85 degrees E } from the towerobserves an angle of elevation pf T to be 11 degrees. Calculate the distance BC between the 2 ppl.

To solve this problem, we can use trigonometry. Let's break down the information given:

1. Point A: The CN Tower
- Height of the CN Tower (TA) = 553 meters

2. Point B: Person in a boat on Lake Ontario due south of the tower
- Angle of elevation from Point B to the top of the tower (angle TBA) = 8 degrees

3. Point C: Another person at a point on a bearing {S 85 degrees E} from the tower
- Angle of elevation from Point C to the top of the tower (angle TCA) = 11 degrees

We need to find the distance between points B and C (BC) using the given information. The key here is to create two right-angled triangles (one with Point A as the top vertex and Point B as the base vertex, and another with Point A as the top vertex and Point C as the base vertex).

In both triangles, we know the height of the tower (TA) and the angle of elevation from the bases (angle TBA and angle TCA).

Using trigonometry, we can calculate the base lengths of both triangles. Let's start with triangle TBA:

In triangle TBA:
- Opposite side = TA (height of the tower) = 553 meters
- Angle of elevation = angle TBA = 8 degrees

We can use the tangent function to find the base length (BA) of triangle TBA:
tan(angle TBA) = Opposite / Adjacent
tan(8 degrees) = TA / BA

Solving for BA:
BA = TA / tan(angle TBA)
BA = 553 / tan(8 degrees)
BA ≈ 4031.48 meters

Now, let's move on to triangle TCA:

In triangle TCA:
- Opposite side = TA (height of the tower) = 553 meters
- Angle of elevation = angle TCA = 11 degrees

Again, we will use the tangent function to find the base length (CA) of triangle TCA:
tan(angle TCA) = Opposite / Adjacent
tan(11 degrees) = TA / CA

Solving for CA:
CA = TA / tan(angle TCA)
CA = 553 / tan(11 degrees)
CA ≈ 3155.59 meters

Now that we know the base lengths BA and CA, we can find the distance BC between points B and C by subtracting the two base lengths:
BC = BA - CA
BC ≈ 4031.48 meters - 3155.59 meters
BC ≈ 875.89 meters

Therefore, the distance BC between the two people observing the CN Tower is approximately 875.89 meters.