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

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15