Use the diagram of the right triangle above and round your answer to the nearest

Option a: is the length of b

Explanation:

The angle of B is and

We need to determine the length of b.

First, let us determine the angle of A.

Since, ABC is a triangle, then all the angles add up to 180°

Thus, we have,

Thus, the angle of A is

Now, we shall determine the length of b using the sine law formula.

The formula for sine law is given by,

where , ,

Thus, we have,

Simplifying, we get,

Multiplying both sides by 0.866, we get,

Multiplying the numerator, we have,

Dividing, we get,

Thus, the length of b is

Hence, Option a is the correct answer.

7.5 pi

Step-by-step explanation:

The formula for arc length of a sector is denoted as

, where x is the central angle of the sector.

Since the sector is 3/4 of a circle, the central angle will be 3/4 of 360 degrees.

3/4 of 360 is 270, so we have our central angle. We also have our radius which we can plug into the formula.

2 times 5 is equal to 10, and 270/360 simplifies to 3/4. 3/4 times 10 is equal to 7.5, so the answer is 7.5 pi