Find the measure of DF in degrees, given that the shaded region has an area of 45.27 square centimeters. If necessary, round your answer to two decimal places.

Question

Find the measure of  DF in degrees, given that the shaded region has an area of 45.27 square centimeters. If necessary, round your answer to two decimal places.

anonymous · Answer

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dtan5457 · Answer

Given the area of the sector, you must first revert the area formula (theta/2)r^2, to solve back for theta (angle degrees)

dtan5457 · Answer

Once you find theta, plug that into the length of an arc formula

(angle E/360 degrees)(2pi(r))

anonymous · Answer

so 45.27/360*2*3.14*6?

dtan5457 · Answer

45.27=6^2(theta)

solve for theta

dtan5457 · Answer

now if i'm not mistaken, theta will be in terms of radians, so convert that to degrees

anonymous · Answer

You lost me at the Theta part

dtan5457 · Answer

treat theta like it's just a variable or x

anonymous · Answer

1.2575 Would it be that?

dtan5457 · Answer

Correct, now converting that to degrees...you get 1.2575x 180/pi

= roughly 72.05 degrees

dtan5457 · Answer

now use the arc formula, you actually just need the 1.2575 part

dtan5457 · Answer

you don't need it in degrees

anonymous · Answer

angle/ 360 degrees = length DF/ 2* pii * r,

anonymous · Answer

So use that?

dtan5457 · Answer

multiply 1.2575 by the radius and your all set

anonymous · Answer

So 1.2575 x 6^2 or 1.2575 x 45.27?

dtan5457 · Answer

your radius is just 6

anonymous · Answer

so my answer would be 7.545 an rounded to two decimal places would be 7.55 Degrees, Units or Units Squared?

anonymous · Answer

@dtan5457

dtan5457 · Answer

pretty sure its just units man

anonymous · Answer

Aight thanks!

dtan5457 · Answer

np feel free to fan and tag me into more q's