# Math Help - skylon tower

1. ## skylon tower

The observation deck of the Skylon tower in Niagera Falls is 166 m above the Nigera River. A tourist on the observation deck notices boat A, which is south of her position, at an angle of depression of 40 degrees. Also, she notices boat B, which is (S70 degrees W) of her position, at an angle of depression of 34 degrees. What is the distance between the two boats?

2. Originally Posted by andrewpark2
The observation deck of the Skylon tower in Niagera Falls is 166 m above the Nigera River. A tourist on the observation deck notices boat A, which is south of her position, at an angle of depression of 40 degrees. Also, she notices boat B, which is (S70 degrees W) of her position, at an angle of depression of 34 degrees. What is the distance between the two boats?
I've attached a sketch of the situation.

1. $\tan(40^\circ) = \dfrac x{166}~\implies~x=166 \cdot \tan(40^\circ)$

2. $\tan(34^\circ) = \dfrac y{166}~\implies~y=166 \cdot \tan(34^\circ)$

3. Now use Cosine rule to calculate the distance d.

I've got 145.8 m