Show that cos - cos /sin - sin = a/b, Mathematics

Assignment Help:

A ladder sets against a wall at an angle α to the horizontal.  If the foot is pulled away from the wall through a distance of 'a', so that is slides a distance 'b' down the wall making an angle β with the horizontal. Show that cosα - cos β/sin β - sin α = a/b

Ans:    Let CB = x m. Length of ladder remains same

Cos α = CB/CA     ∴ ED = AC  Let Ed be

Cos α = x/h       ∴ ED = AC = h

x = hcos α                .........(1)

cos β =DC CB/ED

cos β = a + x/h

a + x = hcos β

x = hcos β - a              .........(2)

from (1) & (2)

hcos α = hcos β - a

hcos α - hcos β = - a

-a = h(cosα - cosβ)      .........(3)

Sin α = Sin α = AE + EB/AC

Sin α =b + EB/ h

hSin α - b = EB

EB = hSin α - b          .........(4)

Sin β = EB /DE

Sin β = EB/h

EB = hSin β             .........(5)

From (4) & (5)

hSin β = hSin α - b

b = hsin α - hSin β

-b = h(Sin β - Sin α)   .........(6)

Divide equation (3) with equation (6)

- a/-b = h(cosα - cos β )/ h(sin β - Sinα )

a/b = Cosα - Cosβ/Sinβ - Sinα


Related Discussions:- Show that cos - cos /sin - sin = a/b

Decimals, how do you turn a fraction into a decimals

how do you turn a fraction into a decimals

Math 100, introduction to decimals

introduction to decimals

Proof of: limq -0 sinq/q = 1 trig limits, Proof of: lim q →0 sin q...

Proof of: lim q →0 sin q / q = 1 This proofs of given limit uses the Squeeze Theorem. Though, getting things set up to utilize the Squeeze Theorem can be a somewha

How many people should she expect not to show, Laura is planning her weddin...

Laura is planning her wedding. She expects 230 people to attend the wedding, but she has been told that around 5% typically don't show. About how many people should she expect not

Horizontal asymptotes, Horizontal asymptotes : Such as we can have vert...

Horizontal asymptotes : Such as we can have vertical asymptotes defined in terms of limits we can also have horizontal asymptotes explained in terms of limits. Definition

Graphs, How do I graph a round robin pool tournment with 6 players using gr...

How do I graph a round robin pool tournment with 6 players using graph theory

Describe order of operations with example, Describe Order of Operations wit...

Describe Order of Operations with example? The order of operations is a set of rules that describe the order in which math operations are done. Try doing this math problem:

Determine the length of the diagonal, A box is 30 cm long, 8 cm wide and 12...

A box is 30 cm long, 8 cm wide and 12 cm high. Determine the length of the diagonal AB ? Round to the nearest tenth. a. 34.5 cm b. 32.1 cm c. 35.2 cm d. 33.3 cm

Find the shortest length of wire needed, A 125-foot tower is located on the...

A 125-foot tower is located on the side of a mountain that is inclined at 32° to the horizontal. A guy wire is to be fitted to the top of the tower and anchored at a point 55 feet

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd