# Math Help - Two questions on Trig. Ratios.

1. ## Two questions on Trig. Ratios.

The two questions are:

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.

7. Suppose Romeo is serenading Juliet while she is on her balcony. Romeo is facing North and sees the balcony at an angle of elevation of 20°. Paris, Juliet's other suitor, is observing the situation and is facing west. Paris sees the balcony at an angle of elevation of 18°. Romeo and Paris are 100m apart as shown at the right. Determine the height of Juliet's balcony above the ground, to the nearest metre.

Here is the actual sheet we were given:
http://img117.imageshack.us/img117/82/help67zz2.png

I don't know how to solve either. Can anyone help? Much obliged.

2. 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: . $x \:=\:CA \:=\:\frac{166}{\tan40^o}$

The tourist looks at boat B . . . The diagram looks like this:
Code:
                    * T
4° * |
*   |
*     |
*       | 166
*         |
* 34°       |
* - - - - - - *
B      y      C
We see that: . $y \:=\:CB \:=\:\frac{166}{\tan34^o}$

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 $d.$

3. Thank you! Now, how do I go about doing 7?

4. Does anyone have a solution?

I hate asking for this, but I'm at a loss.