In the xy-plane above, O is the center of the circle, and the measure of \angleAOB is \pi/a radians. What is the value of a ?

SAT Mathematics Practice Test 2

Question : 19 of 58

Marks: +1, -0

In the xy-plane above,

O

is the center of the circle, and the measure of

∠AOB

π/a

radians. What is the value of

a

Solution:

By the distance formula, the length of radius

O A

√(√3)^2+1^2=√{3+1}=2.

Thus,

sin(∠AOB) =1/2

.Therefore,the measure of

∠AOB

is 30°,which is equal to

30(π/180)=π/6

radians.Hence,the value f

a

is 6

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