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A roof truss is made in the shape of an inverted V The lengths of the two edges are 31 feet and 48 feet The edges meet at the peak making a 63 degree angle. To the ...

Question

A roof truss is made in the shape of an inverted V The lengths of the two edges are 31 feet and 48 feet The edges meet at the peak making a 63 degree angle. To the nearest foot; find the width of the truss and the height of the peak.a =

A roof truss is made in the shape of an inverted V The lengths of the two edges are 31 feet and 48 feet The edges meet at the peak making a 63 degree angle. To the nearest foot; find the width of the truss and the height of the peak. a =



Answers

A truss for the roof of a house is constructed from two identical right triangles. Each has a base of 12 feet and height of 4 feet. Find the measure of the acute angle adjacent to the 4-foot side.

Hello. So here we consider the diagram of the roof here. Now to find the length of the rafter are we can use pythagorean theorem. Um And triangle A. B. D. So we then we have the side A B squared is going to be equal to B. D. Squared plus A. D. Squared. And the span of the roof BC is 36 and B. D. Is 36/2 which is 18. Um A D. Is 12 ft and a B. Is equal to our, so we then have that A B squared or R squared is going to be equal to B. D. Squared. So that's 18 squared plus A. D. Squared. So it's gonna be 12 squared. So therefore r squared is equal to 3 24 plus 144. On other words R squared is equal to 468. So are is going to be equal to them the square root of 468. But that's right. 468 as the product of two numbers with one is a perfect square and 468 is actually 36 times 13. Therefore we have that um are is going to be equal to or the square root of 468. But again, that's right that as 36 times 13, because then this is equal to the square root of 36 times square to 13 square to 36 is six. So therefore are is going to be equal to six times the square root of 13. Um and this is going to be in feet. So here is our exact answer. If you want an approximate answers for that. Um that's going to be about 21 .64 ft.

Okay, so I want to find the length of one of the roofs, right? One side of the roof. Find that on one side of the roof. So I know that this is 36. If this entire 36 this one side, uh, if this entire 36 the single side is going to be 18 the single side is going to be 18 right? Okay, If this is a d and this is 90 can I use the iPod? The news, the spike over a student for the hypotenuse. This is going to be 13.5 square plus 18 square is equal to the site that I won't let me call it X. So this is X square. So let me just use a calculator for this. Just a moment. So what is 13.5 square, 13.5 to 13.5. This is 1 82 0.25 plus 18 square is 3. 24 3 24 is equal to x square. So in order to find eggs, this is 1 82 point 25 I are these two and I take the square root off this. It ain't just a moment. So this is square root off. This is square root off 1 82.25 plus 3 24. So this is 20 to 1 fight. My X over here turns out to be 22.5 ft. My ex turns out to be 22.5 ft. And this is my answer. This is what I want. So this is my answer.

Mr Questions required to find the values off, see and be on deformed the sides off triangle as you can see where the side one of the side is 25 on there are two angles. So what? I would like toa toe another to find DNC. I would use the lows off signs. So first I'll find X, which is the angle here. The third angle and the and this triangle on can be found by taking 118 months 60 miles. 2180 is the summation off the interior angle off this triangle, so X. The angle X is 180. My 60 minus 20. This is 100 now, after I found ex high Can found other Piercy. Since it's already signed X, which is I 100 over 25 equals toe sign 60 Oversee on door sign 20 over Be So let's start with B Sign X, which is 100 over the opposites side. Two X is 25 equals Sign 20 over B because 20 is the opposite to be signed. 20 Overbey, then be as 2500 block by science 20 divided by sine 100. So be equals 8.6 eight feet. Now for see the same, I'll take sign 100 over 25 but instead of 20 are right 60 and oversee. So sign 100 over 25 equals Sign 60 oversea. So see, which is the multiplication off? 25 sign 60 and the product is multiple is divided by sine 100. This gives see to be 21 0.9 eight feet. So these are distributions off this question.

All rights. So this problem describes a building doesn't tell us how tall this building is. But that's my building and has a flagpole on top of the building. And then there's a point out here 330 feet away from the building where they're looking up and they see if they go 63 degrees, they'll see the top of the flagpole if they go 53 degrees to see the bottom of the flagpole. And we want to know how tall is the flagpole, So but I'm gonna D'oh is labeled This f is the height of the fire pole. And then, let's say be, could be the height of the building. Okay, so what I want to do is start by finding be. And to do that, I'm going to say the tangent of 53 degrees equals be over 3 30 So multiply both sides by 3 30 Yeah, that goes. And let's find out what he is So 3 30 times, Tange in 2 53 Make sure your calculators in degrees mode and it looks like B is equal to 437. I'll keep a decimal place or 2 437.92 Great. So keep that off to the side, and I want to clear a little space here and find out what's the height of the whole situation B plus F height of that building and fly pole. So to do that, I'm gonna use the tangent. Ah, 63 and it's going to equal F plus B divided by 3 30 So again, multiply 3 30 on both sides cancels there 3 30 So the flagpole and of the building together are 3 30 times tangent of 63 degrees, which is 647 0.66 That equals F plus B. So, of course, let's subtract be. That is 437 0.92 And over here I'll just call it because those cancel. So for 37.92 that leaves me with flagpole is 209 0.7. And before I write that, let me check. They want the height to the nearest 10th of a foot. So 209.7 huh was 0.741 whatever. So that's how I would round it. And there you go. 209.7 feet


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