Solve each problem.See Examples 3 and 4.

Distance from the Groun...

Question

Solve each problem.See Examples 3 and 4.

Distance from the Ground to the Top of a Building The angle of depression from the top of a building to a point on the ground is 32°30'. How far is the point on the ground from the top of the building if the building is 252 m high?

Accepted Answer

Hello, everyone. We are told an observer from a helipad on the highest level of a building, cites a stone on the ground using a telescope. The angle of depression of the line of sight of the observer is 26 degrees 30 minutes. We want to calculate the distance from the stone to the observer. We are told the building has a height of 118 m and the height of the observer can be considered negligible. We want to round the answer to one decimal place. Our answer choices are a 237.3 m. B 291.4 m C 223.9 m, the 264.5 m. So first, I'm gonna draw a little picture to depict what we're looking at. So I made a vertical line that's green. My building which is 118 m. I'm gonna draw a line that's the ground and put a little stone. And then at the top of my building, I have my observer and his line of sight goes out parallel to the ground and we know the angle of depression. There is 26 degrees, 30 minutes. So since the ground and his line of sight are parallel, I can also say that the bottom left corner has a measure of 26 degrees 30 minutes. Since I want to find the distance between the stone and the observer, that's gonna make my hypotenuse my unknown and I'm labeling it X So now I have an unknown hypotenuse, I have an angle and I have the side opposite it. So when I have opposite and hypotenuse, the first thing that comes to my mind is sign. So I'm gonna find the sign of 26 degrees 30 minutes and that will equal 118 for the side opposite, divided by the hypotenuse, which is X. So rearranging this to get X equals, we'll end up with X equals 118 divided by the sign of 26 degrees 30 minutes. Next, I'm gonna use a calculator to do this math. Make sure your calculator is in degree mode or this will not work out. And when I do so I get that X is approximately 264.457 m. Since we're asked to run to one decimal place, we can round this to 264.5 m. So that is gonna be the distance from the observer to the stone and its answer choice D have a nice day.

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Solve each problem.See Examples 3 and 4. Distance from the Ground to the Top of a Building The angle of depression from the top of a building to a point on the ground is 32°30'. How far is the point on the ground from the top of the building if the building is 252 m high?