The angle of elevation to the top of a Building in New York is found to be 5 degrees from the ground at a distance of 2 miles from the base of the building. Using this information, find the height of the building.

We are given:

Horizontal distance of the point of observation from the building = 2 miles

Angle of elevation of the building = 5 degrees

Finding the height of the Building:

Let the height of the building be x miles

In the given case, the following right-angled triangle will be formed

We know that:  Tan(θ) = Opposite / Adjacent

So, Tan(5°) = x / 2

0.0875 = x/2                                   [since Tan(5°) = 0.0875 ]

x = 0.175                                         [Multiplying both sides by 2]

Height in Meters:

We know that 1 mile = 1609.344 meters

So, we can say that:

1609.344 meters / 1 mile  =  1

Multiplying the height of the building by 1

0.175 miles * 1

since 1 = 1609.344 meters / 1 mile:

0.175*1609.344 meters

Here, the 'miles' in the numerator and the denominator will cancel out

281.6 meters

Hence, the height of the Building is 281.6 m OR 0.175 miles

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!