a cable that is 21 feet long goes from the ground to the top of a building and forms an angle of 40.5 degrees, with the wall of the building. How many feet tall is the building?
You can think about this in terms of a picture, or, a right triangle, to be more accurate. Since the cable goes straight from the ground to the top of the building, you can assume the angle formed between the tower and the ground to be exactly 90 degrees. At this point, you also know the cable’s length is 21 feet. This would serve as your triangle’s hypotenuse. The angle formed between that 21 foot wire and the very top of the building is 40.5 degrees. If we’re thinking about this in terms of a right triangle, you have the ground, the building’s height (which we will call x), and the hypotenuse
which is 21 feet. Furthermore, we also know that the angle formed between the cable and the top of the building is 40.5 degrees. Then we simply look at our given information. We have hypotenuse, but want to find the height, which is the side adjacent relative to the known angle. We don’t know the adjacent length, but we have the hypotenuse and the angle. This prompts us to use cosine, and for our equation (where x is the height of building), we get cos 40.5= x/21. So, the product of cos 40.5 and 21 should give your answer, in feet.