Surveying To determine the distance between two points A end B, a surveyor chooses a point C tha

Surveying To determine the distance between two points A end...

Key Concepts

Surveying

Surveying is the science of determining positions, distances, and angles between points on the Earth’s surface. It involves using various measurement techniques and instruments to gather spatial data for mapping and construction purposes.

Triangle Geometry in Surveying

Triangles are fundamental in surveying as they allow the determination of unknown distances or angles when certain measurements are known. By forming a triangle with measured sides and angles, one can apply geometric principles to solve for other dimensions within the triangle.

Law of Cosines

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is particularly useful in surveying when two sides of a triangle and the included angle are known, allowing for the calculation of the unknown side.

Angle Measurement

Angle measurement in surveying is crucial for accurate calculations. Angles are often expressed in degrees and minutes, and understanding how to interpret and convert these measurements is important when applying trigonometric formulas such as the Law of Cosines.

Transcript

00:01 According to sign rule, if we have a triangle, triangle a, b, c with sides small a, small b and small c, and angles alpha, beta and gamma, as shown in this figure, then we can write sine alpha by a is equal to sine beta by b, that is equal to sine beta by b, that is equal to.

00:32 To sign gamma divided by c.

00:43 In some questions, you will be given the values of angles in the form of degrees and minutes.

00:49 That is for example, m degrees and n minutes instead of just degrees.

00:56 So in order to solve these questions, we need to convert this form into completely degree form.

01:03 That is, for example, m degrees.

01:06 That doesn't mean we have to avoid this minute term.

01:08 But we need to convert that into degrees happen.

01:11 So what do you have to do is that, we know that 1 degree is equal to 60 minutes.

01:19 So dividing both sides by 60, we'll get 1 by 60 degrees is equal to 1 minute.

01:27 Now as we have here is an n minute, so we'll multiply both sides by n.

01:32 So this will give us that is n minutes is equal to n by 1.

01:38 60 degrees.

01:41 So what you have to do is that you just have to divide the values given in minutes by 60 and then it gets converted to degrees.

01:53 And then you have to add this value with this m that is this can be written as m plus n by 60 degrees.

02:06 And then you can solve the question.

02:09 In this question, we are supposed to find the distance between two points, that is a and b.

02:15 We are given the distances from a to c and b to c and the angle alpha according to this figure.

02:23 So angle alpha is 49 degrees and 30 minutes, while a, that is b to c, is 530 yards, and side b, that is a to c, is 375 yards.

02:34 So we are supposed to find c.

02:37 So first of all, what we need to do is that we need to apply sign rule to find the angle beta.

02:44 The reason for that is that we are given the side b and a.

02:49 So we can only find the angles opposite to that sides with the help of sign rule.

02:54 And then only we can find gamma and then c.

02:57 So let's do that first.

02:58 So applying sine rule, sine alpha divided by a is equal to.

03:06 Sine beta divided by b now the first thing that you need to do is that before this the value that is given for alpha is in degrees and minutes we need to convert that into degrees pure degree form for that will be 49 plus 30 minutes that is 30 by 60 will be the total degrees so that means 49 .5 degrees so you need to take this value for alpha so this will become substituting the values sine 49 .5 divided by a is 530 is equal to sine beta divided by 375 so cross multiply we can write sine beta is equal to 375 sine 49 .5 divided by 530 and calculating this we'll get this 375 sine 49 .5 divided by 530 so that will be 0 .5 approximately 0 .54 now as you may know we can have two possible values for beta from this that is beta is equal to sine inverse 0 .54 also beta can be 180 minus sine inverse 0 .54.

04:54 So let's find those two values...

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