Question

A fire hydrant sits 72 feet from the base of a 125 foot tall building. Find the angle of elevation from the fire hydrant to the top of the building

Answer 1

The image attached is an illustration of the scenario given.

Answer:
angle of elevation = 60.058°

Step-by-step explanation:
We can note that the fire hydrant, the building and the line of sight of the angle of elevation together form a right-angled triangle.
Therefore, the special trig functions can be applied.
These functions are as follows:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent

Now, in the given we have:
θ is the angle of elevation we want to find
opposite is the building = 125 ft
adjacent is the distance between the building and the fire hydrant = 72 ft

Therefore, we can apply the tan function to get θ as follows:
tan θ = opposite / adjacent
tan θ = 125 / 72
θ = tan⁻¹(125/72)
θ = 60.058°

Answer 2

see the picture attached to better understand the problem
in the figure C is the fire hydrant

we know that

in the right triangle ABC
AB=opposite side angle x
BC=adjacent side angle x

tan x°=AB/BC-----> 125/72
x=arc tan (125/72)-----> x=60.06°

the answer is
the angle of elevation from the fire hydrant to the top of the building is 60.06°