A hot air balloon rising vertically is tracked by an observer located 4 miles from the lift-off point. at a certain moment, the angle between the observer's line-of-sight and the horizontal is π4 , and it is changing at a rate of 0.1 rad/min. how fast is the balloon rising at this moment?

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.