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

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°

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Louli Louli · Answer 2 · 2018-06-03T14:54:29+02:00

The image attached is an illustration of the scenario given.

Answer:
angle of elevation = 60.058°

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°