Class 10 Maths · Some Applications of Trigonometry · NCERT Exercise 8.4 · Question 15

Some Applications of Trigonometry Hard

A ladder rests against a vertical wall at an inclination

α

to the horizontal. Its foot is pulled away from the wall through a distance

p

so that its upper end slides a distance

q

down the wall and then the ladder makes an angle

β

to the horizontal. Show that

\frac{p}{q} = \frac{cos β - cos α}{sin α - sin β}

Answer

Since

p = L (cos β - cos α)

and

q = L (sin α - sin β)

, dividing gives

\frac{p}{q} = \frac{cos β - cos α}{sin α - sin β}

, as required.

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