A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 6 ft from the wall.)

You are standing 12 feet away from a balloon launcher that will release a balloon vertically up into the air at a raise of 2 ft/sec. When the balloon is 10 feet up in the air, at what rate is the angle changing between the horizontal and the line of sight?

A 10​-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 6 ft from the​ house, the base is moving away at the rate of 24 ​ft/sec. a. What is the rate of change of the height of the top of the​ ladder? b. At what rate is the area of the triangle formed by the​ ladder, wall, and ground changing​then? c. At what rate is the angle between the ladder and the ground changing​ then? A coordinate plane has a horizontal x-axis and a vertical y-axis. A thin rectangle falling from left to right labeled 10 foot ladder starts on the y-axis at y(t) and ends on the x-axis at x(t). An arrow on the y-axis below y(t) is pointing down and an arrow on the x-axis to the right of x(t) is pointing to the right. The angle created between the segment and the x-axis is labeled theta. θ x(t)y(t)010-ft ladderxy   a. The rate of change of the height of the top of the ladder is nothing ​ft/sec. ​(Simplify your​ answer.)   b. The area is changing at…