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10.A safety regulation states that the maximum angle of elevation for a rescue ladder is 720 . Include a well-labeled drawing: (round answers to the tenths place)If...

Question

10.A safety regulation states that the maximum angle of elevation for a rescue ladder is 720 . Include a well-labeled drawing: (round answers to the tenths place)Ifa fire department's longest ladder is 110 feet, what is the maximum safe rescue height? Sin728 Mellos 072 n?104_ LZfr. b.How far away from the building is the base of the ladder?

10.A safety regulation states that the maximum angle of elevation for a rescue ladder is 720 . Include a well-labeled drawing: (round answers to the tenths place) Ifa fire department's longest ladder is 110 feet, what is the maximum safe rescue height? Sin728 Mellos 072 n?104_ LZfr. b.How far away from the building is the base of the ladder?



Answers

According to the Occupational Safety and IIealth Administration (OSIIA), a ladder that is placed against a wall should make a $75.5^{\circ}$ angle with the ground for optimal safety. To the nearest tenth of a foot, what is the maximum height that a 10 -ft ladder can safely reach?

Okay, so in this problem, we have a ladder, and it's resting up against the wall. And so we have a right triangle situation where the floor to wall boundary is a right angle instead of the SaiPan. This here is our ladder, and what we want to know is how high a 20 foot ladder can safely reach. And so we know that this iPod is 20 feet, and we know the angle with respect to the ground is going to be 75 degrees or less. But I'm going to set to 75 degrees since that will be the maximum height that we can reach. If we lower this angle, we're actually going to reach a lower height. But we want the maximum, right. So I'm going to set it to the max one able here. And so we want, uh, this high here. So I'm gonna label that X now the relevant triggered a metric functions used here would be signed since sign of an angle is equal to opposite, which is are unknown, right? It's the X over the hypotheses, which is 20. And so now we can solve this for X multiplying both sides by 20. I get this, and at this point, it's a calculator problem. We go and solve this sign of 75 times 20 and so this is 19.3, and it's gonna be a feat since the 20 here wasn't feet, and that's the answer.

So in this problem, we're setting up a ladder against the building, and my ladder is going to be the hype oddness here. And so you can imagine the rungs of the ladder are kind of like this, not the best artist, So forgive me for that. But anyway, that's our ladder, and we know the maximum angle that it can safely be off the ground. It's 75 degrees. It could be less, but we want to send it to 75 since that's the max angle, which is gonna go Stimac's height here. And the question is asking how far from the building, which would be this distance? I'm gonna call it X. And now let's sell a trigger metric function to solve for X, the one we're going to use this coastline co sign of 75 degrees. And the reason we're using co sign is because it's a Jason and that's gonna be our X to Jason overhyped pot news. And so we have that equation there multiplying both sides by 20 and we quickly get this. And now, at this point, we need to calculator. If you're doing this along with me, make sure that your calculator is in agreement, and so I'm going to do Cup Science 25. Multiply that by 20 and I get five. I need to write better than that. I get five point. Uh, let's just say one A and this is envy, and that's it.

So for this question, we're told that we have any ladder. Those let me up against the wall. We're to the water forms of angles. Six degrees. But the ground so knows this. 19 to study, see references. 30 60 90 triangle. We're told that the waters 18 feet long And so first of all, we're asked how far up the side of building the lot of regions. So we think about their 60 million triangle. Just be accessory to excellence in the X ray three. So we can first find extra extra dressing knife eat over here because it's divided by two. Therefore, we know that for part A, the answer is nine degree, which is approximately equal to see. It's approximately equal, and they want us around two decimal places. So if you type that into our calculator, get approximately 15.59 feet now for Part B. Were asked the horizontal distance from food wired to base building, which we actually already found. But we've dressed knows equal to nine feet, so these are answers

So here we have a problem. We have a building. This is the building windows way. Have a 20 foot ladder leaning against it where it's base, which is This is six feet away from the base of the building. But it s success to figure out first is what's the angle of elevation. So what is this angle here? It's a figure that out. We're gonna be using trigonometry. No, because this is a building. This is a right angle here. So we have six and 26 is adjacent to the theater and twenties thigh positives. So we get the in verse co sign of 6/20 which is equal to what we can do is just calculated with it and clear that nothing is this one. So the universe sign 6/20 72.5 if we round to the first decimal and we can use that to figure out this last side. So because we know that the coastline in the inverse coastline of 6/20 is 72.5 degrees, we can figure out what Sinus, So the sign of 72.5 degrees is equal to our heights of the building are gonna go be over 20 the high positive. So if I plug this into a calculator, the sign of 72.5 we get some 0.95 0.95 is equal to be over 20. So we solved by a B by multiplying 0.95 times 20 and we gets approximately 19.0 second on this isn't feats are gonna put feet, not degrees. So we have. This is our answer for the where the bill ladder is on the building. And this is our angle of elevation, okay, and that's it.


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