Solve each problem.See Examples 3 and 4.

Length of a Shadow Supp...

Question

Solve each problem.See Examples 3 and 4.

Length of a Shadow Suppose that the angle of elevation of the sun is 23.4°. Find the length of the shadow cast by a person who is 5.75 ft tall.​​

Accepted Answer

Hello, everyone. We're asked to calculate the length of the shadow cast by a tower with a height of 114 ft. If the angle of elevation of the sun is 35.2 degrees, we're gonna round our answer to one decimal place. Our answer choices are a 129.4 ft. B 198.0 ft. C 155.3 ft. D 161.6 ft. I'm going to draw a picture to help us solve this problem. So we are talking about the angle of elevation of the sun. So I'm gonna draw myself a little sun and I know that the tower must be between the sun and the shadow. So next, I'm gonna draw a line to represent the tower. It's a vertical line and we know that that has a height of ft. What we need to find is the length of the shadow. So that's gonna go across the bottom and I'm gonna call that X for now, my tower and my shadow should meet at a 90 degree angle. I know my drawing is not perfect, but it should meet at a 90 degree angle. And then our angle of elevation to the sun will be the hypotenuse of this triangle. It will be at the base of the hypotenuse and it's 35.2 degrees. So I have that at the very bottom of the shadow. So now let's see, what do we know, what can we find? We have an angle, we have a side opposite it and we're looking for the side adjacent to it. So thinking about that opposite, divided by adjacent, makes me think of tangent. So we're gonna use the tangent of 35.2 degrees and that equals the opposite side. So 114 divided by the adjacent side which we don't know. So that's X. So now I'm gonna rearrange this so that I have X by itself. So when I do, so I will get that X equals 114 divided by the tangent of 35.2 degrees. So now I'm gonna use a calculator. I'm gonna type all of that in, make sure you are in degree mode or you will not get the right answer. And I get 161. ft. Since we went round to one decimal place, we're gonna round the six that's in the first decimal place. The value to the right of it does not make it round up. So the length of our shadow is 161. ft. And that is answer choice. D have a nice day.

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Solve each problem.See Examples 3 and 4. Length of a Shadow Suppose that the angle of elevation of the sun is 23.4°. Find the length of the shadow cast by a person who is 5.75 ft tall.