A sled travels from point A at the top of a hill to point B at the bottom. If the sled travels 120 m from A to B and the vertical descent AC is 50 m, what is the angle of depression to the nearest degree?
arctan=50/120
you have posted quite a few of these, and I think you have missed them all. Better review the definitions of the basic trig function. For this one, you want
arcsin(50/120)
I agree with Steve. I think you have mis-labeled the diagram. The distance AB is 120m and that is the hypotenuse of the triangle and not the base.
thank you, and my tutor's not very good, and I am home schooled so I have to kind of learn it for myself no one is around to explain it and help me understand I do not have a book due to the budget
money is no excuse. you evidently have the internet. A simple google search will provide oodles of explanations and examples.
One key fact, which I found one of my students was having trouble with: For the purposes of the trig functions, the hypotenuse is not a side!
When looking at one of the acute angles in a right triangle, opposite and adjacent refer to one of the perpendicular sides, not the hypotenuse.
So, consider the angle in question, and its cosine is
adjacentside/hypotenuse
the hypotenuse is also adjacent, but it is not a side in this context.
To find the angle of depression, we can use the inverse tangent function (arctan). The angle of depression is defined as the angle between the horizontal line and the line of sight from the observer (point A) to the object being observed (point B).
In this case, the vertical descent AC is given as 50 meters, and the distance from A to B is given as 120 meters. We want to find the angle of depression.
Using the arctan function, we can write:
arctan(angle of depression) = opposite/adjacent
In this case, opposite is 50 meters (vertical descent) and adjacent is 120 meters (horizontal distance).
Plugging in the values, we have:
arctan(angle of depression) = 50/120
Now, using a calculator or a math software, evaluate the arctan(50/120) to find the angle of depression. The result will be in radians.
To convert the result from radians to degrees, you can multiply it by 180/π. Round the result to the nearest degree, and that will give you the angle of depression.