Question

Find the width, 2x, of the V- Slot shown. Round to the nearest hundredth

Answer 1

The calculated width of the V- Slot is 62.13"

How to determine the width of the V- Slot

From the question, we have the following parameters that can be used in our computation:

The V- Slot

The value of x can be calculated using the following tangent ratio

tan(45/2) = Opposite/Adjacent

So, we have

tan(45/2) = x/75

This gives

x = 75 * tan(45/2)

x = 75 * tan(22.5)

Multiply by 2

2x = 2 * 75 * tan(22.5)

2x = 62.13

Hence, the width is 62.13"

Answer 2

x = half of the width
2x = the full width

Because of this fact, we know that the angle 45 degrees is bisected to get 45/2 = 22.5 degrees

tan(angle) = opposite/adjacent
tan(22.5) = x/75
x = 75*tan(22.5)
x = 31.066017

Multiply both sides by 2 to get
2*x = 2*31.066017
2x = 62.132034
2x = 62.13

Answer: 62.13 inches