The vector v has a magnitude of 89.7 feet and a direction of

12(degree sign)48'. find the magnitude of its vertical component

a: 887.47 ft
b: 19.87 ft
c: 19.38 ft
d: 87.58 ft

Depending on whether the vector makes 12.8° with the horizontal or vertical, the vertical component is

89.7sin(12.8°) or 89.7cos(12.8°) respectively.

thank you!

You're welcome!

To find the magnitude of the vertical component of vector v, we need to use trigonometry.

First, let's convert the angle from degrees and minutes to decimal degrees.

12 degrees 48 minutes = 12 + (48/60) = 12.8 degrees

Now, we can use the magnitude of the vector (89.7 feet) and the angle (12.8 degrees) to find the vertical component of the vector.

The vertical component can be calculated using the formula:

Vertical component = Magnitude * sin(angle)

Vertical component = 89.7 ft * sin(12.8 degrees)

Using a scientific calculator, we can find the sin(12.8 degrees):

sin(12.8 degrees) ≈ 0.2219

Now, we can calculate the vertical component:

Vertical component ≈ 89.7 ft * 0.2219

Vertical component ≈ 19.894 ft

Rounding to two decimal places, the magnitude of the vertical component of vector v is approximately 19.89 ft.

Therefore, the correct answer choice is b: 19.87 ft.