From a point on the ground 2,640 feet from the base of a historic monument, the angle of elevation to its top is 11.87°. To the nearest foot, what is the height of the monument?

The height of the monument is 555ft

Step-by-step explanation:

We have to think of the problem as a right triangle, where the distance from the point to the base of the monument and the height of the monument are the legs

well to start we have to know the relationship between angles, legs and the hypotenuse   in a right triangle

α = 11.87°

a: adjacent  = 2,640ft

o: opposite  = ?

h: hypotenuse

sin α = o/h

cos α = a/h

tan α = o/a

we see that it has (angle, adjacent, opposite)

is the tangent

tan α = o/a

tan 11.87 = o/2,640

tan 11.87 * 2,640 = o

554.89ft

if we want to round to the nearest foot

o = 554.89ft = 555ft

The height of the monument is 555ft

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.

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step-by-step explanation: