50 : ) a dog that has been tethered has a 20 foot lead makes the path shown here. if the length of the path is 45 feet, the measure of angle 0 is radians.

The measure of angle theta is

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

we have

substitute

step 2

Find the measure of angle theta

we know that

The circumference of a circle subtends a central angle of

so

using proportion

Find out the measure of the central angle by a length of arc equal to 45 ft

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

the correct answer is the second option