Homework Help is Here – Start Your Trial Now!
Math
Calculus
A fence 9 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram. Find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. LADDER 9 ft 3 ft a) First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) 9 cos 0 + 3 sin 0 L(0) o [use function notation - use cos(theta) instead of costheta]. sin 0 cos 0 b) Now, find the derivative, L'(0). -2 cos (20)(3 sin(0) + 9 cos 0) + sin(20) (3 cos(0) – 9 sin(0))) 2 cos (0) sin (0) L'(0) = [use function notation - use cos(theta) instead of costheta]. c) Lastly, find the length of the shortest ladder. In other words, minimize the length of the ladder. (Round the answer to 3 decimal places.) L(0min ) - feet

A fence 9 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram. Find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. LADDER 9 ft 3 ft a) First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) 9 cos 0 + 3 sin 0 L(0) o [use function notation - use cos(theta) instead of costheta]. sin 0 cos 0 b) Now, find the derivative, L'(0). -2 cos (20)(3 sin(0) + 9 cos 0) + sin(20) (3 cos(0) – 9 sin(0))) 2 cos (0) sin (0) L'(0) = [use function notation - use cos(theta) instead of costheta]. c) Lastly, find the length of the shortest ladder. In other words, minimize the length of the ladder. (Round the answer to 3 decimal places.) L(0min ) - feet

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 41E
See similar textbooks
icon
Related questions
Question
A fence 9 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram. Find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. LADDER 9 ft 3 ft a) First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) L(0) = 9 cos 0 + 3 sin 0 sin 0 cos 0 o [use function notation - use cos(theta) instead of costheta]. b) Now, find the derivative, L'(0). -2 cos (20) (3 sin(0) + 9 cos 0) + sin(20) (3 cos (0) – 9 sin(0))) L'(0) [use function 2 2 cos“ (0) sin (0) notation - use cos(theta) instead of costheta]. c) Lastly, find the length of the shortest ladder. In other words, minimize the length of the ladder. (Round the answer to 3 decimal places.) L(0min ) feet
Transcribed Image Text:A fence 9 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram. Find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. LADDER 9 ft 3 ft a) First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) L(0) = 9 cos 0 + 3 sin 0 sin 0 cos 0 o [use function notation - use cos(theta) instead of costheta]. b) Now, find the derivative, L'(0). -2 cos (20) (3 sin(0) + 9 cos 0) + sin(20) (3 cos (0) – 9 sin(0))) L'(0) [use function 2 2 cos“ (0) sin (0) notation - use cos(theta) instead of costheta]. c) Lastly, find the length of the shortest ladder. In other words, minimize the length of the ladder. (Round the answer to 3 decimal places.) L(0min ) feet
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Measurement
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS