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A person standing 115 feet from the base of a church observed church"s steeple to be 72 How tall Is the = the angle of elevation t0 the church? (Give your answ...

Question

A person standing 115 feet from the base of a church observed church"s steeple to be 72 How tall Is the = the angle of elevation t0 the church? (Give your answer to the nearest wholc numher)(eet

A person standing 115 feet from the base of a church observed church"s steeple to be 72 How tall Is the = the angle of elevation t0 the church? (Give your answer to the nearest wholc numher) (eet



Answers

Height At a point 50 feet from the base of a church,
the angles of elevation to the bottom of the steeple and
the top of the steeple are $35^{\circ}$ and $47^{\circ}$ , respectively.
Find the height of the steeple.

But we were told that a person a cynic 100 meters away from the Eiffel Tower. So this is our Eiffel Tower. Very badly drawn are fearful Tower. And we're also told the angle of elevation to the top of the Eiffel Tower is 71 0.6 degrees. And so now you're asked to determine what that the height of the Eiffel Tower is. So to start off with, you notice that we're trying to find the height over here, and so we know that. So we're using opposite in our Jason sites, they self over angle. So this tells us. So we're using taint it. So we know that the tangent of 71.6 is eagle tow opposite, which is our heights, which is our unknown over adjacent, which is 100 meters. So because of this, when our height is equal to 100 times the tangent of 71.6, it's so flu. Most my days out, we find that our height is equal to 300 points 61 meters approximately. And so we know that the Eiffel Tower is 300.61 meters tall,

Yeah. Problem number 12 were asked to find the height of the church. So this vertical line I have drawn here is the church to actually figure out the height of the church. This Observer. I have marked over here with that point, oh, is 70 m away from that vertical side of the of the church. So that's the 70 m were also given the angle of elevation is 700.3 radiance. So your angle of elevation is based off the horizontal line from where the observer is. So this is your horizontal to the line of sight. And the line of sight is this line is actually going to go up here, up at that angle. So this angle from the horizontal to the line of sight is your angle of elevation. And that is given to us to be equal 2.3 rats. So I'm going to say, let live equal to the height church. So that means over here, this side is actually going to be equal to the value for why. So I kind of look to see what we're looking for and what we're actually are given this problem, we actually have this angle given to us. And the size that we actually have for these angles is we actually are looking for the side that is opposite of it and were given the side that's actually adjacent to it. So we have the opposite side and we actually have are looking for the opposite side. We're trying to find the adjacent site. So with opposite adjacent, that tells me that I can use tangent to actually do that. I'm gonna take the tangent of my given angle of 0.3 radiance and set that equal to the ratio for tangent, which is the opposite side in this case is why over the adjacent side of 70? So when I multiply both sides by 70 that will give me 70 times the tangent of point three. So when we actually find out the tangent of only that decimal right next to the tangent princes around there. So, um to find out what the Y is equal to, I think 70 multiplied by the tangent of 700.3. It's important that you have to make sure your calculus and actually in the right mode. So make sure your calculus is actually in the radiant mode. And then we do that. We're actually going to take then a 70. We're multiply it by the tangent of 700.3. When I do that multiplication, the Y value cannot because it 21.65 So we're gonna go ahead and around that actually vehicle to 22 ft. So then we actually can say that our height of the church, the height of the church. Mhm is 22. And we're actually we're not in feet. In this problem, we actually are in meters, so actually has 22 meters. Hi, the church is 22 m, based on our trigonometry.

Okay, We're going to sketch the situation so that we can solve for the height of this deep hole. So we have the church and the steeple. We have a point on the ground 50 feet from the church, and the angle of elevation to the base of the steeple, we're told, is 35 degrees and the angle of elevation to the top of the steeple, which would be this entire angle. Here, we're told, is 47 degrees and 40 minutes. We can convert that into 47 2/3 degrees because 40 minutes out of 60 minutes is 2/3 of a degree. Okay, so we're interested in finding why the height of this people. We also are going to have to find X the height of the church without the steeple in order to solve the problem. So let's start with the right triangle at the bottom. We're assuming that the church is perpendicular to the ground and we can use the tangent ratio and write the equation. Tangent of 35 degrees is equal to opposite over adjacent X over 50 that allows us to solve for X X equals 50 times attention of 35 degrees. And let's just leave that exact for now so that we don't approximate it and lose accuracy with our final answer. Now let's work on the big right triangle with the 47 2/3 degree angle, the tangent of 47 2/3 degrees is equal to the opposite over. Adjacent, where the opposite is X plus y on the adjacent is 50. So ultimately, our goal is to solve this equation for why. So it's multiply both sides of the equation by 50 and then subtract X from both sides of the equation. Hoops, that's a plus. So we have 50 tangent of 47 2/3 degrees minus X is equal Dewie. And remember what we found earlier for X 50 tangent, 35. So 50 tangent, 47 2/3 degrees minus 50 tangent. 35 degrees is equal to why. So now is a good time to put this in the calculator all at once. We didn't round anything early, so we shouldn't have lost any accuracy and at this point will get an approximate answer and round, and we get approximately 19.87 feet. That's the height of the steeple

This opponent birds And he went which is related to hide in distance. Do you suppose this is the This is a church. Oh, okay. This is church, and this is a staple. Okay, Okay. Now it is given that angle of elevation from top and bottom. Okay, Bottom and top is 35 degrees and 48 degrees, respectively. So and from a distance from at a distance of 50 ft from the base of the church. So this is 50 ft, and these air then goals off elevations for the bottom and on the top. So this angle of elevation on the bottom is 35 degree top is 48 degree, 35 degrees and this is 48 degrees. So we need to find the value off this. Why? Okay, this is the steeple. I am. So let us right here. A, B, c and D. This is a B c, the church. Maybe this people, we need to find the value off this a b. Let us assume BC as Etch So all are the right angle triangles. So let us start with right angle triangle B C T. In which 10, 35 degree will be equal toe BC by d. C That is at by 50. So that will be equal to 50. Den. 35 degrees will be using this afterwards. Question number one now in a triangle, right. Angled a C D in tangle a C t 10, 48 degree equal toe a C by CD that is a C means why plus at by 50. So why plus as will be equal toe 50 10, 48 degrees. So why will be equal toe? 50 10 48 degrees minus set. So we have, uh, to plug in value of Etch from here from a question number 1 50 10 35 degrees, 50 10, 40 degrees miles 50 10, 35 degrees. Okay, let us take 50 years Common. It will become 10, 40 degrees, minus 10, 35 degrees. So let us use calculator for this calculation. And 48 degrees minus Dan. 35 degrees in 2 50. That is 20.52 Okay, 20.52 So height of the steep early. Approximately. This is 20.52 0 to 4. Okay. I told the steeple approximately is 20.52 ft. Okay. Thank you.


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