Ladder against wall

Geometry Level 4

A ladder rests against a wall at an angle α \alpha to the horizontal. Its foot is pulled away from the wall through a distance a a , so that it slides a distance b b down the wall, making a new angle β \beta with the horizontal. What is the value of a b \frac{a}{b} when α = 6 0 ∘ \alpha = 60^\circ and β = 4 5 ∘ \beta = 45^\circ ?

Give your answer to the first decimal place.


The answer is 1.3.

Rishav Koirala by Rishav Koirala , 22, Singapore

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1 solution

Rishav Koirala
Jul 12, 2016

The problem is a very simple one. It says the ladder moves through a vertical distance of b and a horizontal distance of a when the angle with the horizontal changes from 6 0 ∘ 60^{\circ} to 4 5 ∘ 45^{\circ} . This means the changes in the positions are b and a and not the original vertical and horizontal positions themselves. So, assuming the ladder length is l l , l sin ⁡ 60 − l sin ⁡ 45 = b l \sin{60}-l \sin{45} = b and l cos ⁡ 45 − l cos ⁡ 60 = a l \cos{45}-l \cos{60} = a Divide, solve, and round off the answer to get a b = 1.3 \frac{a}{b}=1.3

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edit the ques to give the ans upto nearest decimal otherwise i kept on entering 1.2 because exactly the calculator is giving the value as 1.2930527 and you aid just enter the first place of decimal.

A Former Brilliant Member - 4 years, 10 months ago

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