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A ladder rests against the top of a perpendicular wall of a building and makes an angle of $73^{\circ}$ with the ground. If the foot of the ladder is $2$ m from the wall.

Calculate:

  • The height of the building,
  • The length of the ladder
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closed as off-topic by MJD, projectilemotion, user228113, Daniel W. Farlow, Simply Beautiful Art Feb 3 '17 at 23:09

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Hint: Let The height of the building be $x$ m and The length of the ladder be $y$ m.

Then apply that $\cos \theta$ is base/hypotenuse and $\tan \theta$ is perpendicular/base.

Here $\theta = 73^{\circ}$.

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In following diagram.

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Let AB length of the ladder. BC length of the wall of building and AC = 2m distance b/w foot of the ladder and wall.

And $\theta = 73°$

$\tan \theta = \frac{BC}{AC}$

Put values and find BC.

$\cos \theta = \frac{AC}{AB}$

Put values and find AB.

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