Right triangle ABC is shown. Which statement is correct?

A) The length of side AB is 6

3

, so the sine of 30° is

3

2

.

B) The length of side AB is 6

3

, so the sine of 60° is

3

2

.

C) The length of side BC is 6

3

, so the sine of 30° is

3

2

.

D) The length of side BC is 6

3

, so the sine of 60° is

3

2

.

The answer to your question is the letter A.  AB = 6√3, sin 30 = √3/2

Step-by-step explanation:

Data

∠C = 60°

hypotenuse = AC = 12

Process

Calculate the length of the sides AB and BC. The calculate these lengths, use trigonometric functions.

a) To calculate AB use sine

           sin Ф = AB / AC

-Solve for AB

          AB = AC sinФ

-Substitution

          AB = 12 sin 60

- Result

          AB = 12√3 / 2

          AB = 6√3

b) To calculate BC use cosine

   cos Ф = BC / AC

-Solve for BC

    BC = AC cosФ

-Substitution

   BC = 12 (1/2)

-Result

   BC = 6

c) Calculate sin 30 and sin 60

   sin 30 = √3/2

   sin 60 = 1/2