A fence 4 feet tall runs parallel to a tall building at a distance of 2 ft from the building as shown in the diagram. LADDER 4 ft We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. [A] First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) Type theta for 0. L(0) [B] Now, find the derivative, L'(0). Type theta for 0. (@).T [C] Once you find the value of 0 that makes L'(0) = 0, substitute that into your original function to find the length of the shortest ladder. (Give your answer accurate to 5 decimal places.)

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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A fence 4 feet tall runs parallel to a tall building at a distance of 2 ft from the building as shown in the
diagram.
LADDER
4 ft
,2 ft
We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall
of the building.
[A] First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.)
Type theta for 0.
L(0) =
[B] Now, find the derivative, L'(0).
Type theta for 0.
= (0).T
[c] Once you find the value of 0 that makes L'(0) = 0, substitute that into your original function to find
the length of the shortest ladder. (Give your answer accurate to 5 decimal places.)
L(0min ) =
feet
Transcribed Image Text:A fence 4 feet tall runs parallel to a tall building at a distance of 2 ft from the building as shown in the diagram. LADDER 4 ft ,2 ft We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. [A] First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) Type theta for 0. L(0) = [B] Now, find the derivative, L'(0). Type theta for 0. = (0).T [c] Once you find the value of 0 that makes L'(0) = 0, substitute that into your original function to find the length of the shortest ladder. (Give your answer accurate to 5 decimal places.) L(0min ) = feet
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