How far from the wall surface must the ladder be moved so that the top of the ladder touches the wall surface 5ft above the floor?

Hi Kayla:

Here"s the method to tackle this kind of problem.

You are watching: A 10 foot ladder is leaning against a wall

First, attract a careful diagram top top the conventional X-Y axes.

Let the basic of the wall be at the origin, O.

Then, the base of the ladder is at suggest P (4. 0) and top the ladder meets the wall surface at allude Q (0, y) - we don"t yet know where the ladder meets the wall.

However, we do understand that ΔOPQ is right angled. So, we have the right to use Pythagoras to find OQ, the distance up the wall where the ladder meets the wall.

Part (a): OQ2 + OP2 = PQ2

OQ2 + 42 = 102

OQ2 = 102 - 42

OQ2 = 100 - 16

∴ OQ = √84

= 2√21

= ~9.17 feet

Part (b) here we need ∠OPQ.

cos ∠OPQ = OP/PQ

= 4/10

=> ∠OPQ = arc cos (0.4)

= 66.42 degrees

Part (c) right here we need ∠OQP = 90 - ∠OPQ

= 90 - 66.42

= 23.58 degrees

Part (d) currently OQ = 5 and also we room asked to discover OP. Again, let"s use an excellent old Pythagoras.

as before, OQ2 + OP2 = PQ2

52 + OP2 = 102

OP2 = 102 - 52

= 100 - 25

=> OP = √75

= 5√3

= ~8.66 feet

upvote • 0 Downvote

include comment

More

Report

## Still looking for help? gain the ideal answer, fast.

questioning a concern for cost-free

gain a cost-free answer come a rapid problem. Most questions answered in ~ 4 hours.

OR

discover an digital Tutor now

pick an expert and also meet online. No packages or subscriptions, pay only for the time you need.

¢ € £ ¥ ‰ µ · • § ¶ ß ‹ › « » > ≤ ≥ – — ¯ ‾ ¤ ¦ ¨ ¡ ¿ ˆ ˜ ° − ± ÷ ⁄ × ƒ ∫ ∑ ∞ √ ∼ ≅ ≈ ≠ ≡ ∈ ∉ ∋ ∏ ∧ ∨ ¬ ∩ ∪ ∂ ∀ ∃ ∅ ∇ ∗ ∝ ∠ ´ ¸ ª º † ‡ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö Ø Œ Š Ù Ú Û Ü Ý Ÿ Þ à á â ã ä å æ ç è é ê ë ì í î ï ð ñ ò ó ô õ ö ø œ š ù ú û ü ý þ ÿ Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω ℵ ϖ ℜ ϒ ℘ ℑ ← ↑ → ↓ ↔ ↵ ⇐ ⇑ ⇒ ⇓ ⇔ ∴ ⊂ ⊃ ⊄ ⊆ ⊇ ⊕ ⊗ ⊥ ⋅ ⌈ ⌉ ⌊ ⌋ 〈 〉 ◊

### RELATED TOPICS

math Algebra 1 Algebra 2 Calculus Precalculus Trigonometry Algebra Word problem Functions Algebra assist ... University Algebra Math assist Math Equations Pre Calculus Precalculus Homework mathematics Ap Calculus Math difficulty Math help For college High school Math aid

### RELATED QUESTIONS

In the equation 3x+2y=9, if x rises by 2 then y walk what?answers · 5

-sin^2=2cosx-2answer · 2

3^(2x)+28=11(3^x)answers · 1

The emphasis of a parabola has collaborates (0,-3/10) and also the vertex in ~ the origin. Discover the equations of the directrix, the axis that symmetry, and also the parabola.answers · 2

y=(x^2-x-2)/(x^2-16)answers · 2

### RECOMMENDED TUTORS

David M.

4.9 (1,550)Priti S.

5.0 (490)Peter K.

5.0 (162)See an ext tutors

### discover an online tutor

Download our totally free app

A link to the application was sent out to your phone.

See more: What Is The Sum Of The Number Of Protons And Neutrons In The Nucleus

Please provide a valid phone number.

Google pat application Store

acquire to understand us

find out with us

occupational with us

Download our totally free app

Google beat application Store

Let’s store in touch

Tabs end spaces!

Need more convincing?

finest in business due to the fact that 2005

Tutors by subject

Tutors by ar

Sitemap regards to Use Privacy policy

© 2005 - 2021 starrkingschool.net, Inc. - every Rights scheduled