Vector v has the given direction angle and magnitude. Find the horizontal and vertical components.

θ = 50°, |v| = 26

Video transcript

Welcome back everyone in this problem. The magnitude and direction angle of vector U are given as 33 and 74 degrees respectively. We want to determine the horizontal and vertical components of the vector. For our answer choices. A says its horizontal component is 9.1 while its vertical component is 31.7 B says the horizontal component is 31.7 and its vertical component is 9.1. C says it's 4.5 and 15.9 respectively. And D says it's 15.9 and 4.5 respectively. Now, in order to figure out the horizontal and vertical components, let's think a little bit about what that means. Let's try to visualize it. So we're saying that we have a vector U. OK? That probably looks something like this where its magnitude or length is 33 units and its direction angle is 74 degrees. That is the angle it makes with the positive X axis in the counterclockwise direction. Now it's horizontal and vertical components if we imagine them here. OK. Let's try it. Its horizontal and vertical components form a right angle because they're perpendicular to each other. And what that tells us then is that we can use what we know about right angle triangles to help us figure out what those horizontal and vertical components are. So let's call its horizontal component UX and let's call its vertical component UI now, since we have our anger here, OK, then we can use what we know about trigonometric ratios because here the vertical component is opposite to a 74 degree angle. So a vertical component is going to be equal to U multiplied by the sine of theta because the sine of an angle equals the opposite side divided by the hypotenuse. Likewise, its horizontal component is adjacent to our angle. And we know that the cosine of our angle is the ratio of its adjacent side to its hypotenuse. Therefore, the horizontal component equals U multiplied by the cosine of our angle. So using that idea then or horizontal component UX is going to be equal to 33 multiplied by the cosine of 74 degrees. And when we put that into our calculator, we should get 9.1. So you should get 9.1 units for its vertical component or its horizontal component rather for its vertical component that is going to be equal to 33 sine 74 degrees and 33 multiplied by the sine of 74 degrees equals 31.7. Therefore, its horizontal horizontal component is 9.1 its vertical component is 31.7 which means that a is the correct answer. Thanks a lot for watching everyone. I hope this video helps.