Question

A ladder leans against the wall at the point B (window end) from a ground level and makes an angle horizontally at 52°. The height of ladder is 15 m. When the same ladder leans above the point B at point A (window start) and makes an angle of 85° horizontally. The distance between point A and point B is *

Answer 1

Given:

The height of the ladder = 15 m

When the ladder leans at point B from the ground level, then it makes an angle  of 52° with the horizontal

When the ladder leans at point A from the ground level, then it makes an angle  of 85° with the horizontal

To find:

The distance between point A and point B is?

Solution:

To solve the above-given problem, we will use the following trigonometric ratio of a triangle:

$\boxed{\boxed{\bold{sin \:\theta = \frac{Opposite\:side}{Hypotenuse} }}}$

Referring to the figure attached below, we will assume,

BD = AD = 15 m = height of the ladder

∠BDC = 52° = angle of elevation to the foot of the window

∠ADC = 85° = angle of elevation to the top of the window

Now,

In ΔBCD, we have

Opposite side = BC

Hypotenuse = BD = 15 m

θ = 52°

∴ $sin\:52 = \frac{BC}{BD}$

$\implies sin\:52 = \frac{BC}{15}$

$\implies 0.788 = \frac{BC}{15}$

$\implies BC = 0.788 \times 15$

$\implies \bold{BC = 11.82 \:m}$

and

In ΔACD, we have

Opposite side = AC

Hypotenuse = AD = 15 m

θ = 85°

∴ $sin\:85 = \frac{AC}{AD}$

$\implies sin\:85 = \frac{AC}{15}$

$\implies 0.996 = \frac{AC}{15}$

$\implies AC = 0.996 \times 15$

$\implies \bold{AC = 14.94 \:m}$

∴ The height of the window, AB = AC - BC = 14.94 m - 11.82 m = 3.12 m

Thus, the distance between point A and point B is 3.12 m.

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