Answered: A 10-ft ladder is leaning against a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 74E

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Question

10-ft

ladder is leaning against a house when its base starts to slide away. By the time the base is

ft from the house, the base is moving away at the rate of

ft/sec.

a. What is the rate of change of the height of the top of the ladder?

b. At what rate is the area of the triangle formed by the ladder, wall, and ground changingthen?

c. At what rate is the angle between the ladder and the ground changing then?

A coordinate plane has a horizontal x-axis and a vertical y-axis. A thin rectangle falling from left to right labeled 10 foot ladder starts on the y-axis at y(t) and ends on the x-axis at x(t). An arrow on the y-axis below y(t) is pointing down and an arrow on the x-axis to the right of x(t) is pointing to the right. The angle created between the segment and the x-axis is labeled theta.

x(t)y(t)010-ft ladderxy

a. The rate of change of the height of the top of the ladder is

nothing

ft/sec.

(Simplify your answer.)

b. The area is changing at

nothing

ft2/sec.

(Simplify your answer.)

c. The angle is changing at

nothing

rad/sec.

(Simplify your answer.)

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