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To find the distance Irom the house at A I0 (ne house afB, surveyor measures the angle ACB; wnich found be 40 and then walks off lhe distance t0 each house, 50 fee...

Question

To find the distance Irom the house at A I0 (ne house afB, surveyor measures the angle ACB; wnich found be 40 and then walks off lhe distance t0 each house, 50 feel and 80 feet, respectively How far apart are Ihe houses?The houses dle Icet apait (Do nol round unta Ine nnal answer Then founa Ihe nearest hunidredinneeded

To find the distance Irom the house at A I0 (ne house afB, surveyor measures the angle ACB; wnich found be 40 and then walks off lhe distance t0 each house, 50 feel and 80 feet, respectively How far apart are Ihe houses? The houses dle Icet apait (Do nol round unta Ine nnal answer Then founa Ihe nearest hunidredin needed



Answers

A surveyor stands 80 feet from the base of a building and measures an angle of $50^{\circ}$ to the top of the steeple on top of the building. The surveyor figures that the center of the steeple lies 20 feet inside the front of the structure. Find the distance from the ground to the top of the steeple.

Hello Friends. In the question It is saying that two ships live live a hardboard suppose Point A is a hard work and two ships are leaving this hardboard with the angle of 1 35 degree 40 minutes. Okay? And they travel 402 Both. Okay. So after this distance, the what is third of distance between these two saves is asking for us. Okay. So the first safety is on Point B. Second champions on Point C. And we have to find the distance between point B. And say that is busy. Okay? So we know in a triangle abc the this is the side A. Mm This is a side this is see so the value of C. Is 40 to so the value of B. S. 402 Because the angle the angle be a positive side is called? Being the angle, see opposite side is called C. And the angle a opposite side of his called So we can now see that B. C. Is a close to air and which we have to fight. Okay so because I intrude, we know that A. Is queries equals to be Squire. Pless C. Is choir minus two B. C. Course E. Who we know all that E. Sorry we know the value of B. C. N. A. So we will put this value here and we can find them the value of A. That is a line bees in the value of line Pc. Okay so and in the question there is given the angle is 1 35 point 1 35 degree and 40 minutes. That is called minute. Okay so first we need to simplify this. This means 1 35 degree plus 40 minutes. So when one degree has 16 minutes that means 40 dick. 40 minutes should have 45 60 degree. Okay because. Mhm. Because fun degree is it close to for is it goes to 60 minutes? Okay so 41 one minute is equals to one by 60. So 40 minutes will be for B. Y. 60. Okay so we put this with this value here. So on solving this weekend 1 35. Bless two by three degree. Okay now if we simplify this we get 1 35 plus 0.67 degree. That is 1 35.67 degree. The value of A. Is this now again by coarsened you'll be no is quite as opposed to B squared plus C. Square minus to B to C. Of course. Now we know all the values from here. We substitute all values. The value of P is 20402 Mhm. To the power to 402 to the power to into two into 402 into 402 Of course 1 35 point 67 degree. Okay so from here you can take common 4 62. 402 to the power one then it will be one plus one minus two. Into course 1 35 0.6 73. Okay so the level of 462 is 402 to the power to. Okay and this is two minus to into cause 1 35.67 degree is minus zero 0.71 two. Okay so this will be for zero to minus minus Bliss place to into 0.1705 Okay this degree is not no on simplifying this week it is queries 55 43 17.72 Okay so this is the value of a square. So the value of A will be under route 55 4301.72 That is seven 44.5. So the value of B. C. Will be 4744.5. Okay. That's that means that they're they're they're different. The distance between two ships will be 1744.5.

In this question figure has been provided using which we need to approximate the distance between two points P and Cube. So for that purpose let us first reconstruct that figure there is a triangle. Mhm. Where these two points are the points P and cute. Mhm. And the other end of the triangle is that point are. It has also given that the length of pr is 300 ft And the length of the side RQ is given to be 438 ft. Also, the angle over here and a P R Q is given to be 37 degrees and 40 minutes. Now we need to approximate the distance between P and Q. That is we need to determine the length of the side. You let this side E. Let this side be considered as B. And let this side be considered A. C. And let this anger be assumed to be equal alpha. Then using the law, of course science will get a square is equal to the square policy square minus two Bc. Times called alpha. So from here we can obtain that E. Is equal to the square. Who will be square Policy square minus to B. C. Times calls off. So now we just need to substitute these values. So this would be going to root over be square. So that would be 300 square. Let's see square. So that the 438 square minus two times B, which is 300 times C, which is 4 38. And with that we multiply cause of alpha alpha being 37 degrees and 40 minutes. So we just need to calculate the square root of this value and the value of this is approximately equal to 271.7. And since the unit for the distances of the other sides are and feet, this will also be in feet. So the approximate distance between P and Q is 271.7 ft

This is limited to 20 in which there is a surveyor who wants to measure the distance between A and B and B, and he goes toe through a point C one C, which is 420 yards from a and 520 yards from B. So, like this, says, see, 420 years from mhm and 514 yards from B angle is also being given as a C B 63 degree in 10 minutes. This angle a C B is 63 degree and 10 minutes. We need to approximate the value of a B, since it is the two sides and including is being given so we can use or we will be using the design law toe. Get the value of a B. According to cosign law, we will become Is he squired, bless busy squired minus two into a safe distance into BC Distance cause and go A C B. So let's plug in the values for 20 whole square plus 540 year old square. He mhm minus two and 2, 422 540 cause 63 degree, 10 minutes. Okay, now We have to use a calculator for this. Okay, this comes out to be 500. Okay? Okay. Not 500. 1st lay. It will be okay. 263246 point for three for three. Okay. And it's the Squire. It will be 513.754 So a B is approximately a wage approximately, we can say 513.1 yards. What? This is a dancer. Thank you so much.

And there are two house and ah, the shapes and positioned off this to house Looks like a part off branch off the hyper Bhola and ah, we need to find ah, the distance between their clothes. This point. So, as you see here, if the position off this house looks like ah branch off hyper bola Ah, the closest points will be the between their birth disease. Remember the hyper bulla? So that is here. We need Teoh. Find the length off transfers access eso Let's find first of all, the burgesses coordinate off the birth disease. So the equation is given as you see And by using the equation off the hyper bola, we will get it. So here it is not in the standard for so the ratched right side should be one we needed the white all turns by Ah, to 150,000 year the white 250,000. So you're so so uh I mean divide and simplify. We will get ah y squared over 400 miners X squared over 625 equal one. And as you see here, um, the arms off high parabola up and down to the origin. According to why exes? That's transfers access on the Y axis. So it means that here a square is 400. So ese cool toe to any. So the coordinate off burgesses will be One of them is here on the Y axis zero and 20 and the other one will be zero and negative 20. So the distance between the Vertex is, as you see two times to any two times doing it, that is 40 yards.


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