CONCEPT PREVIEW Match each equation in Column I with the appropri...

Question

CONCEPT PREVIEW Match each equation in Column I with the appropriate right triangle in Column II. In each case, the goal is to find the value of x.

I                                         II
1.                              A.   B.   C. 
2.                              
3.                              D.   E.   F. 
4.
5. x = 5 sin 38°
6.

Accepted Answer

Everyone in this problem, we're asked to draw a right triangle that has a side link given by the following equation X is equal to 10 multiplied by sine of 47 degrees. Now, we know X is a sideline. We've been told that and what we wanna do is take our equation X is equal to 10 multiplied by sine of 47 degrees and rewrite this as sine of our angle is equal to something. And that's how our trigonometric ratios are defined sine is equal to opposite divided by hypotenuse. And so if we rearrange this equation, it's gonna be easier to pick out what our triangle should look. So let's rearrange. And when we do that, dividing by 10, on each side, we get sign of 47 degrees is equal to X divided by 10. Now recall when we have sign of an angle, OK. This trigonometric ratio is defined as the opposite side divided by the hypotenuse. So let's start drawing our triangle and we have this right angle triangle and it makes a 90 degree angle. We know that we're gonna have an angle of 47 degrees. That's the angle we're given and then looking at this rearranged trigonometric ratio that we've written, we know the opposite side to this angle is going to be X. So we look at our angle, we look to the opposite side that's going to be X and similar, similarly, the hypotenuse. So that side across from our 90 degree angle is going to be 10. As we have a right angle triangle, we have the angle of 47 degrees with the opposite side of X A hypotenuse of 10. And that is a right triangle that has that side length given by the equation we have. That's it for this one. Thanks everyone for watching. See you in the next video.

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CONCEPT PREVIEW Match each equation in Column I with the appropriate right triangle in Column II. In each case, the goal is to find the value of x. I II 1. A. B. C. 2. 3. D. E. F. 4. 5. x = 5 sin 38° 6.