Question

Which of the following is the vertical component of a vector that has a direction angle of 0 =115º and a magnitude of 0.5? Round your answer to the nearest hundredth.

Answer 1

We are told that the vector has an angle of 115° and a magnitude of 0.5. We can imagine this as follows

We are asked to find the vertical component of the vector. That is, the y coordinate of the point that is located at the tip of the vector. Note that we can draw a triangle using the vector. The vector would be the hypotenuse of the triangle, with a length of 0.5. And the other sides of the triangle correspond to the horizontal and vertical magnitudes. To determine the vertical magnitude, we should first find the angle theta. Note that, from the picture

`\theta+115=180`

Then, by subtracting 115 on both sides, we get

`\theta=180-115=65`

So we have the following triangle

WE are given the length of the hypotenuse, and the angle of the triangle and we are interested in the length of the opposite side. So, we will use the sine ratio. Recall that for an angle in a right triangle

`\sin (\text{angle)}=\frac{\text{lenght of opposite side}}{length\text{ of the hypotenuse}}`

So in our case, we have

`\sin (65)=(y)/(0.5)`

So, if we multiply both sides by 0.5, we get

`y=0.5\cdot\sin (65)\approx0.4531`

Since the vector is pointing up, we are sure that the y coordinate should be positive.