question archive A tree trunk is inclined at a 60? angle to the ground
A tree trunk is inclined at a 60? angle to the ground
Subject:MathPrice: Bought3
A tree trunk is inclined 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.
(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.
Please also explain how to do each step and write write proportionality relation on part B.
