If @ lies between 0⁰ and 180⁰ and sin@ is 0.5 find the two possible values of @?

Since sin@ = 0.5, we know that @ must be either 30⁰ or 150⁰.

This is because sin(30⁰) = 0.5 and sin(150⁰) = 0.5.

Therefore, the two possible values of @ are 30⁰ and 150⁰.

Step 1: Find the reference angle

Since sin@ is positive, the angle @ must lie in the first or second quadrant.

The reference angle (α) is the acute angle formed by the positive x-axis and the terminal side of @.

We have sinα = |sin@| = 0.5

From the unit circle, we find that α = 30⁰.

Step 2: Find the two possible values of @

In the first quadrant, @ = α = 30⁰.

In the second quadrant, @ = 180⁰ - α = 180⁰ - 30⁰ = 150⁰.

Therefore, the two possible values of @ are 30⁰ and 150⁰.