Question

Building A is 490 feet tall and Building B is 754 feet tall. If the angle of depression from the top of Building B to the top of Building A is 46°, how far apart are the buildings?

Answer 1

Answer: $254.94\ ft$

Step-by-step explanation:

Given

Building A is 490 feet tall and building B is 754 ft tall.

If the angle of depression from building B to the top of building A is $46^{\circ}$

Difference in the height of the two buildings is $754-490=264\ ft$

If the difference between them is $x$

From the figure, we can write

$\Rightarrow \tan 46^{\circ}=\dfrac{264}{x}\\\\\Rightarrow x=\dfrac{264}{\tan 46^{\circ}}\\\\\Rightarrow x=254.94\ ft$

Therefore, the two buildings are $254.94\ ft$ apart.