Question

Building A is 480 feet tall and Building B is 654 feet tall. If the angle of
depression from the top of Building B to the top of Building A is 42°,
how far apart are the buildings?

Answer 1

Answer:

The buildings are 193.2444 feet apart

Step- by- step explanation:

As shown in the diagram, the magnitude of CE shows how far apart the buildings are.

Using trigonometry ratio,

$\tan(48) \degree= \frac{ |CE| }{174}$

$tan(48) \degree\times174=|CE|$

$|CE|= 1.1106\times174$

$|CE|=193.2444$

Hence the buildings are 193.2444 feet apart

Answer 2

Building A and building B are 193.24 feet distant from each other.

Given that:

• Building A is 480 feet tall.

• Building B is 654 feet tall.

• Angle of depression from B to A's top is  42°

To find:

How apart are the buildings?

How can we calculate how apart are the buildings?

Building B is 654 - 480 = 174 feet taller than Building B

Let the distance between both buildings is d. Then:

The angle we take will be complement of  angle of depression, thus 90 - 42 = 48 degrees.

From the viewpoint of that angle, the distance between building is perpendicular and the difference between buildings is the base of the right triangle.

Thus,

$tan(48^{\circ}) = \dfrac{d}{174}\\\\1.11 = \dfrac{d}{174}\\\\d = 1.11\times 174\\\\d = 193.24 \: \rm feet$

Thus, both buildings are 193.24 feet distant from each other.

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