The diagram represents the circular floor under the dome of a state capitol building. the diameter is 40 feet. find the area of the floor. use 3.14 for π.

1256 ft^2

Step-by-step explanation:

Area (A) of a circumference is A = π*r^2, where r is the radius of the circumference.

Taking into account that r = D/2, where D is the diameter of the circumference, therefore, the area formula can be written as

A = π*r^2

A = π*(D/2)^2

π*(D^2)/4

For this exercise, the diameter is 40 feet, hence

A = π*(D^2)/4 = 3.14*(40^2)/4 = 1256 ft^2

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)