Question

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

a. 35° angle of depression
b. 49° angle of depression
c. 80° angle of depression
d. 87° angle of depression
e. 89° angle of depression
f. 89.9° angle of depression
g. What appears to be happening to the slopes (and tangent values) as the angles of depression get closer to 90°?
h. Find the slopes of angles of depression that are even closer to 90° than 89.9°. Can the value of the tangent of 90° be defined? Why or why not?

Answer 1

a. -0.7002

b. -1.1504

c. -5.6713

d. -19.0811

e. -57.2900

f. -572.9572

g. As the depression angle approaches 90 degrees, the slope module appears to quickly grow.

h. For 89.99° angle of depression, the slope is -5729.5779. The value of the tangent for 90° is 0°.

Explanation:

For items from a. to f. simply compute

`\tan\left(-35\deg\right)=-0.7002`

g. The trend clearly shows how this value "explodes".

h. Can be determined from a conceptual point of view, since involving a line with infinite slope makes nonsense calculations.