Question

From the top of a 200 meters high building, the angle of depression to the bottom of a second building is 20 degrees. From the same point, the angle of elevation to the top of the second building is 10 degrees. Calculate the height of the second building.

Answer 1

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Answer 2

The height of the second building is 296.96 meters.

Given:

According to the rough figure attached below;

The height of the first building (CD) is = 200m.

The angle of depression to the bottom of the second building (AB) is ∅ = 20°.

The angle of elevation to the top of the second building is Ф  = 10°.

To Find:

The height of the second building (AB) =?

Solution:

The above-given problem is based on the topic of Basic concepts of Trigonometry.

As given in the figure below, we will apply trigonometric equations in the triangles BCD and AEC.

First of all, let us assume the horizontal distance between the two buildings i.e., BD is 'd'.

Now, applying the tangent formula in the ΔBCD, we get;

i.e., tan (∅) =  $\frac{CD}{BD}$

⇒  tan (20°) = $\frac{200}{d}$

⇒  0.363 =  $\frac{200}{d}$

⇒  d =  $\frac{200}{0.363}$

⇒  d =  550.96 m.

Again, applying the same formula in the ΔAEC, we get;

i.e., tan (Ф) =  $\frac{AE}{EC}$

⇒  tan (10°) =  $\frac{H}{d}$

⇒  0.176 =  $\frac{H}{d}$

⇒  H = 0.176 × d

⇒  H = 0.176 × 550.96

⇒  H = 96.96 m = AE

The total height of the second building (AB) = AE + BE

i.e.,  AB = 96.96 + 200

AB = 296.96 m.

Therefore the height of the second building is 296.96 meters.

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