Question

the angle of elevation of the top of an unfinished verticle building on a ground, at a point which is 100m from the base of the building is 45 degree. How much height the building be raised, so that its angle of elevation from the same point be 60 degree. (Take root3 =1.73)​

Answer 1

the building to be raised is 73 metre

then the total height of the building becomes 173metre

Answer 2

The height of building raised by 73 m when the angle of elevation from the same point is 60 degree.

Step-by-step explanation:

CD=100 m

In triangle BCD

$\theta=45^{\circ}$

$\frac{BC}{CD}=tan45$

Using

$\frac{Perpendicular\;side}{Base}=tan\theta$

$\frac{BC}{100}=1$

$BC=100 m$

AC=AB+BC=AB+100

In triangle ACD

$\theta=60^{\circ}$

$\frac{AC}{CD}=tan60$

$\frac{AB+100}{100}=\sqrt 3$

Using $tan60^{\circ}=\sqrt 3$

$AB+100=100\times 1.73=173$

Using $\sqrt 3=1.73$

$AB=173-100=73 m$

Hence, the height of building raised by 73 m when the angle of elevation from the same point is 60 degree.

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