Question

Question 34, the answer is C. I just need the working. Tysm

Answer 1

C

Explanation:

∠ ABC = 90° ( angle in a semicircle )

Using the cosine ratio in right triangle ABC and the exact value

cos30° =
`(√(3) )/(2)` , then

cos30° =
`(adjacent )/(hypotenuse)` =
`(AB)/(AC)` =
`(10)/(AC)` =
`(√(3) )/(2)` ( cross- multiply )

AC ×
`√(3)` = 20 ( divide both sides by
`√(3)` )

AC =
`(20)/(√(3) )` ×
`(√(3) )/(√(3) )` ( rationalising denominator )

AC =
`(20√(3) )/(3)`

radius AO =
`(1)/(2)` AC =
`(1)/(2)` ×
`(20√(3) )/(3)` =
`(10√(3) )/(3)` → C