From a small boat at the sea the angle of elevation to the top of the cliff, 128m above sea level, is 28 degrees. After rowing directly towards the cliff, it's angle of elevation from the boat is found to be 46 degrees. How far did the boat travel while being rowed towards the cliff?

Answer 1

Let's call the distance the boat traveled towards the cliff "x".

Then, using trigonometry, we can set up the following two equations:

(1) tan(28) = 128 / d, where d is the distance between the boat and the base of the cliff before rowing towards it. We can rearrange this equation to solve for d:

d = 128 / tan(28)

(2) tan(46) = 128 / (d-x), where (d-x) is the distance between the boat and the base of the cliff after rowing towards it.

We can substitute the expression for d from equation (1) into equation (2):

tan(46) = 128 / (128 / tan(28) - x)

Now we can solve for x:

x = 47.8 meters (rounded to one decimal place)

Therefore, the boat traveled approximately 47.8 meters towards the cliff.

Answer 2

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