solve-the-given-problems-a-surveyor-measures-the-distance-between-two-markers-to-be-37800-mathrmm--2

Question

Solve the given problems.
A surveyor measures the distance between two markers to be $378.00 \mathrm{m}$. Then, moving along a line equidistant from the markers, the distance $d$ from the surveyor to each marker is $d=189.00 \csc \frac{1}{2} 	heta,$ where $	heta$ is the angle between the lines of sight to the markers. See Fig. 27.6. By using differentials, find the change in $d$ if $	heta$ changes from $98.20^{\circ}$ to $98.45^{\circ}$.

Carson Merrill · Accepted Answer

for this given problem, we have a surveyor measuring the distance between two markers and then moving along the line equidistant. So we see that the distance is going to be, I&#x27;m called D. F kovacs can be 1 89 co second of one half. They don&#x27;t mind escapes packs. So we want to find the change in B if they had changes from 98.2° To 98.45°.. So based on this, we see that a minor change is going to be F of 98.45 minus F of 98.2. And that&#x27;s provided by 98.45 98 point Let me get about a negative 53 .71. So you see that&#x27;s going to be the slope. Um And based on that, we see that negative 53.7 or negative 54 will end up being the rate of change approximately from 98.2°- 98.45°.. We want to keep in mind that this is going to be in Degrees, so in this case it will actually be about negative 1.88 as the slope, but everything else holds the same.

Ethan Somes · Answer

So in this question, were trying to find the distance between two people. We know that one person over here can see the other person who is six with two in the distance. They know that when they look at them, the angle between the other person&#x27;s head and feet is zero degrees. In 37 minutes. We want to try and find out how far apart they are. So we&#x27;re really trying to find the radius here of this circle so we can use our formula s, which is our our Klink equals our ankle measure and radiance times Air radius Insult for that radius marinara arc length is six foot two. Let&#x27;s just put that all of which is so six feet two inches the same as well, six feet times 12 inches each, plus two extra inches is going to give us 74. Just so our argument 74. That&#x27;s Quentin most kind fire angle measure. Give us, um, radius would consult for us or 37 minutes. That&#x27;s actually 37 60th of a degree, and we can multiply that to make radiance. We got a multiplied by higher Etienne&#x27;s over 100 beauty degrees to give us our, um, number of radiance of this 37 60. It&#x27;s times pi over one e t is going to give us zero points. 01 076 and I&#x27;ll stop there. Old ground for now. Radiance. So now we know that 74 inches d Call Syria point 01076 radiance times are radius. So we&#x27;re going to 74 divided by 0.1 76. You know, 10 76 brothers to go there. No one ever up 75 of 74 that is going to give us our radius. And when I saw that out I am going to get 6000 875 0.49 inches. And if I turn that back into feet by dividing by 12. 6875.49 divided by 12 that&#x27;s going to give us approximately 573 feet away. So a person there observing is about five opportunity 73 feet away from the original person

Robert Daugherty · Answer

Section 55 Number 37. So they give us an application problem. The key is just reading the problem, drawing a diagram and labeling what you know. So they tell us that there&#x27;s a canyon and two markers a n B. On the same side of the canyon. Those markers are 56 feet apart, and they tell us 1/3 marker see is located across this canyon, and it forms an angle. So angle B A C. It&#x27;s 72 degrees and then also forms angle. ABC. So angle ABC is 53 degrees now. They want us to find what is the length of a C. So this is the side that I am after in this particular case. So can I use the law of sign in order to use? A lot of Sinai would need to identify an angle and an opposite side that I know. Here&#x27;s the opposite side, so I would need to know angle see? Well, that&#x27;s pretty straightforward. So angle see, it&#x27;s just going to be 1 80 minus 70 to minus 53 so that is 1 80 minus one 25 and that it&#x27;s just going to be 55 degrees. So I know that this angle see right here is 55 degrees. So to solve for this side that I do not know I know that X divided by the sine of 53 degrees. That&#x27;s going to be equal to 56 divided by the sine 55 degrees, which tells me that this side X is going to be 56. Sign of 53 divided by the sine of 55. So 56 sign of 53. So 56 times the sign of 53 divided by. And that was the sign of 55. Uh, the sign 55. So that gives me 54.59 54 points. 597 So I&#x27;m going to get this side a c. It&#x27;s about 54 with that 54.597 and that was measured in feet. The next thing they asked us was to figure out then what is the distance between the two canyons? Assume that they are parallel so on. I&#x27;m assuming they&#x27;re saying, find the shortest distance. So that means what would be the distance between these two canyon. So we&#x27;re gonna form two right triangles there and then I have a couple choices of how to do this. Um, the the side that I know already I know Side X. So I could say, Well, what is a relationship? It&#x27;s the sign of A is going to be whatever this side here that I do not know, it&#x27;s gonna be a chew over X. So I know that the sign of a that&#x27;s going to be a church over X, which I just figured out. So it tells me that h is going to be that&#x27;s what, 54 0.597 times the sign of 72. And that would give me the shortest distance of 54.597 times a sign of 72. So 54 point 54.597 times the sign handle with that angle with the sign of 72. So that gives me 51.9 of 51.93 so 51 0.93 feet. That gives me the shortest distance. So that is the measure of this distance from here to here. And then the measure A C was that first distance that we ended up obtaining

Melissa Salvador · Answer

Okay, so here we have a lighthouse or to light house 1.8 when a point B. And so we are told that there is a ship, Um uh, at a bearing of 129 degrees and 43 minutes from, like house A. And then it is also at a bearing off 39 degrees and for three minutes from, um, not house be. And so the ship is sitting right here, and from there we want to find this distance from the two lighthouses so x that I have labour here. So the first thing you want to do is, um, turned his degrees in minutes into the greeting decimal. So this will be 1 to 9 plus 43 over 60 which is equal to one. 29.716 degrees. And then we have 39 plus 43/60 which is then equal to 39.716 Okay, so now what I want to do is find this angle right here. So we&#x27;re gonna do 1 80 minus 1239.746 We get that every equal 50.28 and so degrees. I want to use that angle to find X. The next thing that we&#x27;re going to do actually Sorry is fine what this angle is. So we&#x27;re gonna dio 1 80 minus the 50.28 miners that 39 1716 indicated that equals 90. So we have a right triangle. Okay, So because of that, we can use our feathery and Oh yeah, sorry are to econometric identities. And so I want to use this angle right here we have It&#x27;s adjacent side and we have the high partners we want to use. Co site goes I know 50.28 is equal to adjacent overhype pot use. So for X and we get the X would be five 1008 156 meters.

Ankit Gupta · Answer

So in this question, I have an observation tower here and power Bi. They&#x27;re observing an airplane moving something like this. So this is the airplane P. Okay, so it is given to me that the separation between them is two miles on notice that this angle list heat other mentioned on this angle is mentioned to me. Yes. Fight. So the first thing that we are going to do let B p is equal toady? No. In the next time, I&#x27;m going to a place in law for saying lock in this triangle. If I have to say one thing we mentioned here is this angle quickly. I can comment. It will be five minus Tita. So some off interior angles is equal to exterior angle using that So saying love and I were playing. I&#x27;ll see BP divided way scientists is equal to the opposite side so that the store divided by signing off five minus Tita. So BP, which I told it as the days a photo I&#x27;d like to 70 30 right away, saying off five minus Tita. All right, so in the last step, when he ties given to me as 40 degrees and fires given to me a 60 degrees. I love these equal toe to sign. 40 degrees divided way. Science. 20 degrees. All right, so this can be simplified. As so this one will be obtained US 3.7 five. So therefore, I&#x27;ll finally conclude that the distance between the plane and point being plane on point B is a corridor 3.758 miles. So that&#x27;s my answer.

Melissa Salvador · Answer

Okay, So you got a lake and also Bayer. And so we give in two different angles and length from the surveyor to the lake. Um, this is 53.1 meters and said we want to find that this system went into the leg to the other one. So we want to find this right here so we can choose whatever angle we want. I&#x27;m gonna choose this one right here. And so first we want to convert this into degree. Wouldn&#x27;t decimal. So this would be 32 plus number 60 which is then just equal to 32.16. And so we have the side opposite and the side adjacent. So we&#x27;re gonna be isn&#x27;t tangent. Teoh engine off 32.16 is equal to our present, which what? We want to find the let&#x27;s call this X so X over adjacent 53.1. So we&#x27;re gonna multiply by figure 3.1 bullet sides, and then we would get that, um X would be 33.4 meters

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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Basic Technical Mathematics with Calculus