Hello, Jeavus!

6. The observation deck of the Skylon Tower in Niagra Falls, Ontario,

is 166m above the Niagra River.

A tourist in the observation deck notices two boats on the water.

From the tourist's position:

. . the bearing of boat A is 180° at an angle of depression of 40°.

. . the bearing of boat B is 250° at an angle of depression of 34°.

Calculate the distance between the boats to the nearest metre. A three-dimensional trig problem . . . ack!

The tourist looks at boat A . . . The diagram looks like this: Code:

T * - - - - - -
| * 40°
| *
166 | *
| *
| *
| 40° *
* - - - - - - *
C x A

We see that: .$\displaystyle x \:=\:CA \:=\:\frac{166}{\tan40^o}$

The tourist looks at boat B . . . The diagram looks like this: Code:

* T
4° * |
* |
* |
* | 166
* |
* 34° |
* - - - - - - *
B y C

We see that: .$\displaystyle y \:=\:CB \:=\:\frac{166}{\tan34^o}$

Looking straight down at the ground, we have this diagram: Code:

C
*
* *
* 70° *
y * * x
* *
* *
* *
* *
* - - - - - - - - - - - *
B d A

Now you can use the Law of Cosines to find the distance $\displaystyle d.$