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Points and B are separated by a lake To find the distance between them_ sunyevor ocates point land such than ZCAB = 51.2 Find the distance across the lake from_525 ...

Question

Points and B are separated by a lake To find the distance between them_ sunyevor ocates point land such than ZCAB = 51.2 Find the distance across the lake from_525 wd5k2*380 ydNOTE: The trlangle Is NOT drawn t0 scale.distanceEnter your answer 05 number; vour onset should be accurate to decimal places _

Points and B are separated by a lake To find the distance between them_ sunyevor ocates point land such than ZCAB = 51.2 Find the distance across the lake from_ 525 wd 5k2* 380 yd NOTE: The trlangle Is NOT drawn t0 scale. distance Enter your answer 05 number; vour onset should be accurate to decimal places _



Answers

Distance Across a Lake Points $A$ and $B$ are separated by a lake. To find the distance between them, a surveyor locates a point $C$ on land such that $\angle C A B=48.6^{\circ} .$ He also measures $C A$ as 312 $\mathrm{ft}$ and $C B$ as 527 ft. Find the distance between $A$ and $B .$

We have problem number 46. It is from the chapter of a solution of right angles in the trigonometry. Okay, so we have to find the distance are as across the lake and RT some distances are being given. Okay, so let us right some distances and some angles are being given. Yes, this is the figure this S. R. R. S. T. Okay. And we have been provided some some uh distances and some parameters R. T. Is 53.1 m. So this is given 53.1 m. And we have angle t equal to 32° 10 minutes. And As equal to 57 degree And 15 minutes, we have to find RS. So this we need to find if we add these two angles, it will be T. Plus as equal to ah 189° and 60 minutes, which makes it 90°.. So the rest angle that is remaining angle are must be equal to 90 degree. Hence the strangle RST must be a right angle triangle. Okay, now we have to find this and this uh, angle T. Is being given. So we'll be utilizing tea and we'll be using tangent T equal to S. R. That is perpendicular, oppose it. Bye. Arty. Okay, I settled artists. Yes. Rs. We should. Right artist. Okay. So from here R. S. Will be equal to RT into then the tangent of tea. So, uh, let's plug in. The values are T. 53.1 m. And this is attendant. He is 32° 10 minutes. By using calculation, we will be getting dan 52 degree and 10 minutes and into 50 frequent one m. So this will be 33 39 five. So we have the length R. S. That is distance Required distance approximately equal to 33 points 395 And it was seven tour also 72 meters. Thank you so much. This should be the answer.

We have problem number 46. It is from the chapter of a solution of right angles in the trigonometry. Okay, so we have to find the distance are as across the lake and RT some distances are being given. Okay, so let us right some distances and some angles are being given. Yes, this is the figure this S. R. R. S. T. Okay. And we have been provided some some uh distances and some parameters R. T. Is 53.1 m. So this is given 53.1 m. And we have angle t equal to 32° 10 minutes. And As equal to 57 degree And 15 minutes, we have to find RS. So this we need to find if we add these two angles, it will be T. Plus as equal to ah 189° and 60 minutes, which makes it 90°.. So the rest angle that is remaining angle are must be equal to 90 degree. Hence the strangle RST must be a right angle triangle. Okay, now we have to find this and this uh, angle T. Is being given. So we'll be utilizing tea and we'll be using tangent T equal to S. R. That is perpendicular, oppose it. Bye. Arty. Okay, I settled artists. Yes. Rs. We should. Right artist. Okay. So from here R. S. Will be equal to RT into then the tangent of tea. So, uh, let's plug in. The values are T. 53.1 m. And this is attendant. He is 32° 10 minutes. By using calculation, we will be getting dan 52 degree and 10 minutes and into 50 frequent one m. So this will be 33 39 five. So we have the length R. S. That is distance Required distance approximately equal to 33 points 395 And it was seven tour also 72 meters. Thank you so much. This should be the answer.

We have a problem. Number 15. Okay, Way have to find. Yeah, the distance A and B. Her point b is in the lake and aids on the shore. Okay, No problem. So we have been provided with certain things that angle PBS 65 degree. So this is 65 degree angle. APB is 25 degrees and be a three ended 52 m. So we have to find the value off a p. So if you look at the angles and properties this angle, let's suppose x x place 25 degrees plus 65 degrees equal to 180 degrees. So x place 90 degree in one day to degree. If you subtract 90 degree from both the sides, X will be 90 degrees. So we have this angle as 90 degree, which means this is a right triangle, this right angle and the angle, and this is right triangle so we can take any angle 25 degree of 65 degrees to calculate the value off a B. Now this is this will be the hyper tennis. And if we consider 65 degree so 65 for 65 degrees the opposite leg will be PB and happiness is B A. So if you take sad, Okay. 65 degrees, which is apposite. That is BB by AP. So Phoebe is okay. We need to find a B. No need to take sign. We should take costs. Because, of course, we will be included. Okay, No problem. We should take costs 65 degrees or signed 25 degrees. So let us take cost 65 degrees cause 65 degrees that it just sent. It doesn't means Okay, We have a B by Appleton ears AP. So a B will be equal to AP cause 65 degrees. Okay, So a be equal to a P. We have 352 and to cause 65. Have you calculated 352 in two? Okay, let's say it is in really in more so it is first. Okay, Yes. 352 inches. Two cause 65 degrees. That is one of the 48.76 148 point 761 So distance between a B is approximately 148 point 76 m. Thank you so much.

We have our number 17. Sorry. 57 in which, uh, we have to find the distance across the lake. That s our or others. Okay, It's severe. Lays off art equal to 53.1 m. That this is 3 to 3.1 m with angle. T t angle is given is being given as 32 degree 10 minutes and angle s is 57 degrees 15 minutes. We have to find the length artists this length. So now, since two angles and a side is given, So we will be using sign law which say's sign off angle T divide bell are as equal toe sign off angle s divide by rt, which means our s will be equal toe rt in tow. Okay, sign t by. Sign s Okay. This is the value of r s. Okay. Is it cool? Yes. Okay. So let's plug in the values so ours will be equal. Toe rt means 53.1 m into science. T that is science. Uh, D. 32 degrees. 10 minutes. Divide by side. 57 degree, 50 minutes. So we have to use calculator. So r s will be 53.1 in two. Let us get those values signed. But two degrees. 10 minutes. Okay. 32 disease, 10 minutes. Divide by sign. 57 degrees, 15 minutes. Signed. 57 degrees Place. 0, 50 minutes. That is open 6 to 89 The weapon 6 to 892 Okay. In 2. 53.1. Territory, 3.3957 33.39 57 Okay, so the distance required distance R s across the lake approximately will be called toe 33.4 m. Thank you so much.


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