Point C moves along the top arc of a circle of radius 1 centered at the origin O(0, 0) from point A(-1, 0) to point B(1, 0) such that the angle BOC decreases at a constant rate 1 radian per minute. How does the area of the triangle ABC change at the moment when |AC|=1? Answer: it increases at 1/2 square units per minute. Could you give me a hint how to solve this task? I don't even know what to begin with.

Question

Point C moves along the top arc of a circle of radius 1 centered at the origin O(0, 0) from point A(-1, 0) to point B(1, 0) such that the angle BOC decreases at a constant rate 1 radian per minute. How does the area of the triangle ABC change at the moment when |AC|=1? Answer: it increases at 1/2 square units per minute. Could you give me a hint how to solve this task? I don&#039;t even know what to begin with.

stigliy0 · Accepted Answer

Say angle   B  O  C is   θ. Express the area of triangle   A  B  C in terms of   θ (use sin). This is an area   A in terms of   θ. Find             d      A              d      θ      .Then find the point where   C  A  =  1 and determine   θ at that point. Evaluate             d      A              d      θ       for that value of   θ.

polivijuye · Accepted Answer

and then use the chain rule to obtain             d      A              d      t        =            d      A              d      θ        ∗            d      θ              d      t

Point C moves along the top arc of a circle of radius 1 centered at the origin O(0, 0) from point A(

Answered question

Answer & Explanation

New Questions in High school geometry