Lee is on a cliff 360 m above sea level, the angle of depression of a ship is 28 degrees. To the nearest meter, what is the distance between the ship and the base of the cliff?
Would this be set up 360/tan28 due to it being the angle of DEPRESSION?
correct
Yes, you are correct. To find the distance between the ship and the base of the cliff, you can use trigonometry and specifically the tangent function. Here's how you can set up the calculation:
Let's denote the distance between the ship and the base of the cliff as x.
The tangent of the angle of depression (28 degrees) is equal to the opposite side (360 m) divided by the adjacent side (x). So the equation is:
tan(28) = opposite / adjacent
tan(28) = 360 / x
To find x, you can rearrange the equation:
x = 360 / tan(28)
Now, you can plug this into a calculator to get the numerical answer. Rounding to the nearest meter, the distance between the ship and the base of the cliff is approximately 594 meters.