Find the measures of the angles in the truss shown in Fig. 2. 14 . A truss is a rigid support st

step 1 Welcome to Numerid. In the current problem, we have to find what is angle BDF. Okay. Now, here i

Find the measures of the angles in the truss shown in Fig....

Key Concepts

Truss Structures

A truss is a framework typically composed of triangular units that are connected at joints to form a rigid structure. This concept is crucial in engineering because it allows the distribution of loads and supports in buildings and bridges, ensuring that forces are efficiently managed throughout the structure.

Angle Measurement in Geometry

Determining the measure of an angle involves assessing the rotational displacement between two intersecting lines or segments. In the context of a truss, correctly measuring angles is essential for verifying the integrity and design of the structure, as precise angles dictate the distribution of forces and overall stability.

Triangle Geometry

Triangles are fundamental to the design of truss structures due to their inherent stability. Key properties such as the angle sum theorem—which states that the interior angles of a triangle add up to 180 degrees—are used to calculate unknown angles, ensuring that each triangular component functions correctly within the framework.

Transcript

00:01 Welcome to numerid.

00:02 In the current problem, we have to find what is angle bdf.

00:10 Okay.

00:11 Now, here is the one.

00:13 You can find out what this is bdf.

00:16 Okay, so you have to find this.

00:18 But before we proceed with that, we have to see what is given.

00:22 So given is a -f parallel b -e.

00:25 That means this entire a -f is parallel to b -e.

00:29 Correct okay and it is also given that this angle b c e are 90 degrees okay now based on that you you just can't find uh find uh give a statement like okay i can see this de and this ac is also looking like they are parallel so maybe they are parallel no we cannot make assumptions like that okay so if we are telling that we have to come with some statement some theorems or some ready results that will help you to say so.

01:06 In geometry, we just can't upfront give a statement that this looks like that.

01:11 This logic, you just check it out in the first itself so that you can think of something new, some new logics.

01:17 For example, if i ask you what is the measurement of this angle, your instinct will be like, it's 90 degree, which is true.

01:25 But you just can't see because it looks 90 degree, because it could be 89 degrees, and 89 degree, 90 degree and 91 degree will look all the same with our bear eyes.

01:37 So, geometry always deserves logic.

01:40 This is a place that trains your brain for logic.

01:43 So, since abc, like a, a, c, f, this we will refer as the biggest triangle.

01:53 The biggest triangle is having a right angle, correct? so, of course, a, b and cf, they are perpendiculars, right? and this angle is given to be 90 degree.

02:08 Now, since ac is one side, this is a straight angle, this entire angle is 180 degree, correct? so if one side of this angle is 90 degree, what should be the other side? the other side will also be 90 degree, right? so this angle will be 90 degree.

02:27 Using similar logic we can show this angle also will be 90 degree so now look at the quadrilateral d b c e in d b c e we see this angle is the last angle left and in a quadrilateral some of all that angles will be 360 so for quadrilateral d b c e angle d plus angle b c e angle d plus angle c plus angle e will be 360 whereas except d so and except angle d angle b angle c is 90 so i will directly substitute 90 and angle e would be t e c or ced that's not this will be 360 degree now what is angle d b b c this is nothing but 180 degree minus angle d b a so 180 degree minus angle d b i'm not directly writing 90 degree because we did not derive it anywhere so it's always better to have explanations ready in correct place so that we are not deducted so d e f now here you you may write since ac a c is a side of the given triangle acf, angle a, c, f, angle a, b, c is equal to 180 degree, which implies angle d, b, a, plus angle d, b, c is equal to 180 degree.

04:48 And same for angle dec.

05:02 That means we can proceed on the same line.

05:06 So, thereby we are able to prove that angle d plus, now angle dba is dba is 90 d.

05:18 Which is given already, right? so i will just clear the diagram first.

05:26 So this would be.

05:31 Minus 90 plus 90 plus 180 minus 90 is equals 360 0 now this 90 90 90 cancels this 180 180 1080 so we will have angle d is equals to 90 degrees so we came till here now for angle d b f if you remember we have to find bd...

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