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To estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is
30
∘
. From a point that is 150 feet closer to the building, the angle of elevation (at ground level) to the top of the building is
52
∘
. If we assume that the street is level, use this information to estimate the height of the building.

The height of the building is feet.

Respuesta :

Answer:

h = tan(52 degrees) * (d - 150)

Step-by-step explanation:

Angle of elevation from the first point: 30 degrees

Angle of elevation from the second point: 52 degrees

Distance difference between the two points: 150 feet

Using basic trigonometry:

From the first observation, we can express the relationship between the height of the building (h) and the distance from the first observation point to the building (d) as follows:

The tangent of the angle of elevation (30 degrees) is equal to the ratio of the height of the building to the distance (h/d).

From the second observation, we can express the relationship between the height of the building (h) and the distance from the second observation point to the building (d - 150) as follows:

The tangent of the angle of elevation (52 degrees) is equal to the ratio of the height of the building to the distance minus 150 feet (h/(d - 150)).

Now, solving the second equation for h:

We can rearrange the equation from the second observation to solve for h:

h = tan(52 degrees) * (d - 150)

These equations provide a means to determine the height (h) of the building by solving for d and subsequently substituting it into the equation.