Question

Analyze the diagram below and complete the instructions that follow. Find a, b, and c.

Answer 1

The correct answer is the letter C.

Explanation:

We can use the following trigonometric identity:

`cos(60)=(6)/(b)` (1)

`cos(45)=(c)/(b)` (2)

Solving each equation by b and equaling we have:

`(6)/(cos(60))=(c)/(cos(45))`

`(6)/(cos(60))=(c)/(cos(45))`

Let's recall that:

`cos(45)=(1)/(√(2))`

`cos(60)=(1)/(2)`

Then we have:

`c=(cos(45)*6)/(cos(60))`

`c=(2*6)/(√(2))`

`c=(12)/(√(2))`

`c=6√(2)`

Using equation (1) we can find b.

`cos(60)=(6)/(b)`

`b=12`

Finally, we can find a using the next equation:

`tan(60)=(a)/(6)`

`a=6*tan(60)`

`a=6√(3)`

Therefore, the correct answer is the letter C.

I hope it helps you!