Question

# Letter to a Friend: Problem 3 (3 points). A tree trunk is inclinded at a 60° angle to the ground. The top end of a ladder rests against the trunk at a distance of 2 feet from its base. The bottom end rests on the ground(assumed to be horizontal) at a distance of 11 feet from the trunk's base. The trunk leans directly toward the ladder, so that the trunk, ground, and ladder form a triangle with a 60° angle. form a triangle with a 60° angle.(a) Use the law of cosines to write an equation that relates the distances from the ends of the ladder to the base of the tree. Do not solve this equation for either of the two variables. Include an accurate picture. Be sure to define your variables in complete sentences. (b) Use implicit differentiation to determine the proportionality constant that lets you approximate the change in the distance from the bottom end of the ladder to the tree's base in terms of a small change in the distance from the top end to the base. Then write the proportionality relation. As usual, craft your response in the form of a letter to a friend. Points will be deducted for responses not in this form.  Fig: 1  Fig: 2  Fig: 3  Fig: 4