Given the angles of depression below, determine the slope of the line with the indicated angle correct to four decimal places

Question

The angles of depression given are:

1. 35° angle of depression
2. 49° angle of depression
3. 80° angle of depression
4. 87° angle of depression
5. 89° angle of depression
6. 89.9° angle of depression

This is on my final review but we haven't learned about this, so if someone could please explain how to do it this and find the slope, thank you.

Also, we just started talking about angles of depression and elevation with right triangles and word scenarios involving right triangles, but I have a question, don't the angle of depression and angle of elevation equal each other because alternate interior?

Answer 1

While a given size of angle of depression and inclination would seem to equal each other, they cannot be treated the same when it comes to calculating slope, which is change in y divided by change in x...the changes in x would be identical but the changes in y would have opposing signs. You can determine the changes in x and y by taking the cosine and sine of each angle in question, respectively, and from that figure the slope.