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A ladder leaning against a window of a building is 10 feet long and forms an angle of elevation of 18 degrees Ifit is replaced by a ladder forms an angle of elevati...

Question

A ladder leaning against a window of a building is 10 feet long and forms an angle of elevation of 18 degrees Ifit is replaced by a ladder forms an angle of elevation of 12 degrees, how long is the new ladder if it reaches the same point on the window? (Round to the nearest hundredth)_

A ladder leaning against a window of a building is 10 feet long and forms an angle of elevation of 18 degrees Ifit is replaced by a ladder forms an angle of elevation of 12 degrees, how long is the new ladder if it reaches the same point on the window? (Round to the nearest hundredth)_



Answers

A ladder 18 ft long leans against a building. The ladder forms an angle of $60^{\circ}$ with the ground. (a) How high up the side of the building does the ladder reach? [Give two forms for your answer: one with radicals and one (using a calculator) with decimals, rounded to two places. $]$ (b) Find the horizontal distance from the foot of the ladder to the base of the building.

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

This is all a number 50 in which letters given which leaning against the wall. Okay, so if this is a wall Uh huh and we have a letter. So the length of the letter is given 20 ft. 25th letter is leaning against the wall so the wall must be perpendicular. This is a This is B. This is C. And one more thing is given that the letter is the letter is 6 ft away from the building. So this has given us 6 ft. So we have to find the angle kita and the value off it valuable of a B and will support this to the X. So in right angle triangle, Right angle triangle, ABC. This We have to find the value off this X so we can use the bicycle serum that is a C square, which you have transit square equal to a B square plus B C square. So a C square is 20 square, equal to a be a square access choir plus 60 square, 400 equal toe access squad plus 36. Yeah. Access choir will be equal toe 400 minus 36. That is 364 x will be called toe Squire route off 364 364 that in 19.0 78 Okay, the day this is 19.78 So we have the letter leaning against the wall at almost at a height off approximate height, 19 point 08 ft. Okay, now we have to find angle theta. So let us use these to the foreign Guilty that this is a descent and this is the have 14 years. So cause theater cause theater will be just sent. Buy happiness that is three by 10. So theater will be cool toe cause in verse three by 10 Off course inverse 0.3 like 72.5542 72 point 54 degrees. So the letter is leaning against the wall at an angle off 72.54 degrees

So a 20 foot ladder is leaning ace the building. So it's leaning right here. So that's 20 feet. And the base of the ladder is six feet from the base of the building. All right, so we have this here is six feet and we need to find the angle of elevation in the height. So six feet here and let's take this s data. So what's the angle of elevation? Well, in this case we have are adjacent. We have an adjacent value for the site and we have the high pot news. So in this case, we're going to use co sign, so co sign data is six over 20. So now we use co sign inverse off 6/20 to find Fada. So Fada is equal to a co sign in verse 6/20 and our angle of elevation is 72 point five degrees, 72.5 degrees here. So that's our Angus answer for angle off elevation. Now, the height we confined the height with two methods, we can use their Pythagorean theorem. Uh huh. Or we can use the angle. But that's just go is the Pythagorean theorem. So 20 squared minus six squared is equal to H squared. So 20 squared is 400 minus 36. So square root that the height H will be 19 0.1 feet, So this will be your height.

All right. Welcome back for this problem. We have the loading ramp conforms in England. 18 degrees. You don't know how high it is, but was quarter H and it is 10 feet bond. This is gonna be replaced by a new, um, loading room. We don't know how long it will be that evil for running off 12 degrees from the horse under What is this length? All right here. Well, first what? Sold for this smaller triangle right here. You know that this is 90 degrees Ah, 180 degrees, minus 90 degrees. This 1990 miles 18. I would give us 72 I believe. Yeah. Looks like 72 degrees. Okay, Um, no. Using that, we can find this height h so, 10 um, divided by Did you involve signs? Say 90 is equal to H. Very sign, uh, 18 degrees. Senator McCain is just one with more people sites by a sign of 18. All right, so this high, right here it is. He courting you? Um, 3.0 nine heat. Okay, so now we know that this I hate this height right here. You know this Ingrid, Here's talk preaches this is stole many degrees, but that would make this larger angle under this in a different color will poop. It's larger angle right here. Um, B 78 degrees, seven th degrees. Okay. And if that's 78 degrees, very confused. A lot of signs again, Mr. Since we know H is equal to 3.9 So 3.9 If I did buy sign 0 12 degrees, it's equal to L over. Sign of 90 degrees. Centre manager Chris is just one that would mean to go equal to three concerning do better by sign. So the length of the new room will be 14 point a fortune 0.9 feet one, uh is a freelancer.


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