Answer:
135 degrees
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference is equal to
we have
substitute
step 2
Remember that the circumference of the circle subtends a central angle of 360 degrees
so
using proportion
Find out the measurement of the central angle (in degrees) that intercepts an arc with a length of 9π/2 ft
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Work Shown:
Check out the diagram below. Note the pair of alternate interior angles that are congruent (each 37 degrees). Then focus on triangle ABC. With the reference angle being at A, this means we use the tangent function because BC = x is the opposite side and AB = 97 is the adjacent side.
tan(angle) = opposite/adjacent
tan(A) = BC/AB
tan(37) = x/97
97*tan(37) = x
x = 97*tan(37)
x = 73.094742859971
For the last step, you'll need a calculator that can handle trig functions. Make sure the calculator is in degree mode. The result here is approximate. This rounds to 73 when rounding to the nearest whole number.
