The base of an isosceles triangle 10 feet long and the base angles are decreasing at a rate of 2 degress per second. Find the rate of change of the area when the base angles are 45 degrees?
Here in the figure BC=10ft. And we assume (cause isosceles triangle).
Also BD=DC=5ft (cause AD is the perpendicular bisector of BC).
Now, in , using trigonometry:-
So, now we calculate the area of the :-
Now, as we're dealing with rate of change of different stuff we differentiate both sides wrt :-
We, put , and use the rate of change of given in the question.
So, rate of change of area is sq ft per second.
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