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.
If the person is due south and the tower is 553m, then the distance of B from the tower is
tan(8deg)=553m/dist. to B -you should be able to solve for the distance to B.
You should be able to determine the distance from C to the tower too as
tan(11deg)=553m/dist. to C -you should be able to solve for the distance to C.
You should now know the distance each is from the tower and the angle between the two points. You should be able to find the distance bewteen B and C using one of your trig identities, like oh say, the law of cosines or something similar.
To calculate the distance BC between points B and C, we can use the Law of Cosines.
First, let's find the distance from point B to the tower. We already know that the angle of elevation at point B is 8 degrees and the height of the tower is 553m. We can use the tangent function to find the distance to point B.
tan(8 degrees) = 553m / distance to B
Solving for the distance to B:
distance to B = 553m / tan(8 degrees)
Next, let's find the distance from point C to the tower. We already know that the angle of elevation at point C is 11 degrees and the height of the tower is 553m. We can again use the tangent function to find the distance to point C.
tan(11 degrees) = 553m / distance to C
Solving for the distance to C:
distance to C = 553m / tan(11 degrees)
Now that we know the distances from both points B and C to the tower, let's calculate the distance BC using the Law of Cosines. The Law of Cosines states:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case:
a = distance to B
b = distance to C
c = distance BC
Since we want to find BC, we rearrange the formula:
c^2 = a^2 + b^2 - 2ab * cos(C)
Plugging in the known values:
BC^2 = (553m / tan(8 degrees))^2 + (553m / tan(11 degrees))^2 - 2 * (553m / tan(8 degrees)) * (553m / tan(11 degrees)) * cos(85 degrees)
Now, we can calculate BC by taking the square root of both sides:
BC = sqrt[(553m / tan(8 degrees))^2 + (553m / tan(11 degrees))^2 - 2 * (553m / tan(8 degrees)) * (553m / tan(11 degrees)) * cos(85 degrees)]
Using this formula, you can now calculate the distance BC between the two people.