Aladder 10 ft long rests against a vertical wall. if the bottom of the ladder slides away from the wall at a rate of 1.3 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (that is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.)

The angle's rate of change when the bottom of the ladder is 8ft from the wall is

It is given the Length of Ladder is . and the distance between the bottom of the ladder to the wall is as shown in the below figure.

By using the Pythagoras Theorem

and

Differentiating both sides with respect to by using the chain rule

given

putting this in eq.1, we get

So the angle's rate of change when the bottom of the ladder is 8ft from the wall is.

Know more about Pythagoras Theorem here:

link

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)

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