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From an observation polnt A, forest ranger sights fire in the direction 535850W. Frorn point B, miles due west of another ranger sights the same fire In the directi...

Question

From an observation polnt A, forest ranger sights fire in the direction 535850W. Frorn point B, miles due west of another ranger sights the same fire In the direction 554810E The two observation points and the point where the= fire located form triangleApproximate, to the nearest tenth of a mile, the distance d of the fire from A

From an observation polnt A, forest ranger sights fire in the direction 535850W. Frorn point B, miles due west of another ranger sights the same fire In the direction 554810E The two observation points and the point where the= fire located form triangle Approximate, to the nearest tenth of a mile, the distance d of the fire from A



Answers

Sighting a forest fire A forest ranger at an observation point $A$ sights a fire in the direction $\mathrm{N} 27^{\circ} 10^{\prime} \mathrm{E}$. Another ranger at an observation point $B, 6.0$ miles due east of $A$. sights the same fire at $\mathrm{N} 52^{\circ} 40^{\prime} \mathrm{W}$. Approximate the distance from each of the observation points to the fire.

Way we're going to do. Question 53 which states that the Forest Ranger sights fire directly to the south. Ah, second Ranger. It's seven miles east off the fest. Ranger also size the same fire. The building from the Second Ranger. So the fire is this 28 degrees west. How far to the nearest tanks? Off the mound is the first Ranger for the fire. Um, basically, we're going to craft this sketch off that provided information as there is no money. The kiss, uh, where they're doing. Hearing you start with your North North is very important. Saxo is our sister, Ranger. This is where origin is. The origin is the position off the Observer. So that's where our origin is with The Ranger is holding. Let's call it Rachel. What? Justin? Too Jewish. So he cites a fire. Uh, which is, uh, which is exactly so days in flying. The fire is south on and it so happened that the second is a second ranger. Well, he's about seven miles Ah, directly to the east. So there is a ranger too. Who is East Watts? So, Besar, just remember this is our soft. This is our guest. So Ranger Two is seven miles away. And now what we also are given is that is beer into the fire. So basically, I need to draw the north again. In order for us to do bad. We have to sketch the North days are not. And if you extended in love, uh, you also created the South Days, the South. It's not very important. But it's important in so far is the hearing is consent. Okay, so this is where our son of years So Adam, to a little mission. Tow my wife. I don't want these on the West, so they're worth decided. He's also the Eastside with me looking for Caroline. Therefore, we are given that the hearing to the fire, which is this. Let me a troll. Yeah. So the beer ng tow the fire is 20 is if 28 w So you're coming from the south, Then you go to where their degrees to the west south in line. Is this one trained? A ridiculous To the west. There we go. And this is 28. Now. If that is truly eight, it means that this one the interior and goto that triangle that is formed is, uh, 90 degrees my industry in the age. So the interior Anglo is nine to decrease my last 28 decrease, and that gives us about 62 degrees. Okay, so we we have what we want or domestically, once we have the system to with enough information, what we need is that distance. Let's call it why? So that's why distance what you're looking for. And we have got the 60 to decrease given seven miles. So in terms off the Given Anglo 62 why is opposite and seven miles is adjusted, So we're going to use the ratio with opposite It's tangent and that ratio is ton. So we can say Ton 62 is equal to opposites all over. I'm Justin. And then what we do is then we I multiply both sides by seven. Then this in that goes and then with what? Why you cost seven ton 60 to decrease, which, if we use our complete I'll get 18.165 which is rounded off to the nearest tent, is stating 0.2 miles

According to question, We have this type of condition. First, we tried rather diagram. Here we have the building from the fire to the second Ranger is north 28 degree. It means this angle is given equal to 20 degrees and using a right triangle, the known angle. And we have a known accorded side that is given equal toe seven miles, and we have an unknown at the sensor. It let's see that is given equal toe be then using attention function, then off 28 degree is equal to seven, divided by be. It implies that B is equal toe seven, divided by 10 off, 28 degrees are per simplifications, and we get B is approximately equal to 13 point toe minds. It means the first stranger is 13.2 miles from the fire. So the nearest plant off Mike

Okay, so we are discussing applications of trick functions, and we have a four strangers sites of fire directly to the south. Okay, so here is the forest Ranger. And here is the fire, and it's directly south. The bearing. So a second ranger seven miles east of the First Ranger. So here's the second Ranger. This distance is seven miles. The bearing from the second Ranger to the fire is south 28 degrees west. So this bearing here is south 28 degrees west. So that means this is 28 degrees. We need to know how far to the nearest 10th of a mile is the first ranger from the fire. So we know that if this is our triangle here, let me get a different color. So this is the triangle that we need. This bottom distance is seven miles, because it's seven miles up here and we need to know how far is the first ranger to the fire. So we need this distance, which gives us this side. Okay, so now, using the trick that we know we can use the tangent. So tangent is opposite over adjacent. But we could also use so if we have, The tangent of Fada is equal to the opposite, which is seven miles over the adjacent, which is what we need to find. So notice that theano angle is 28 degrees, but it's pointing down into the left, so that's 90 minus 28 degrees, so X is equal to seven times tangent of 90 minus 28 degrees, and this is equal to 13.2 miles.

Okay. So we look at the graph. Okay. The fire observation platform A. Is that minus 6 10 and B. Is that 60 in the fireplace Is located at sea which is 48. So let's calculate the distance between A and C. And B and C. So we have four minus minus six Squared plus 8 -10 squared. And we take the square root in which he calls the 10 squared plus minus two squared within the square roots. So we have 104 and we take the square root. Now let's cancel the distance between B and C. So we have 6 -4 squared plus. They're old minus eight squared. Take the square root. This is a close to four plus 64. Take the square root is square root off 68. Okay. Obviously the distance between B and C is smaller than smaller than distance between A. And C. Okay, so we say observation tower B. It's closer to the fire. Yeah.


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