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A tree casts shadow 31.8 feet long: If the angle of elevation from the tip of the shadow to the sun 378 how tall is the tree? Round final answer t0 the nearest tent...

Question

A tree casts shadow 31.8 feet long: If the angle of elevation from the tip of the shadow to the sun 378 how tall is the tree? Round final answer t0 the nearest tenth;

A tree casts shadow 31.8 feet long: If the angle of elevation from the tip of the shadow to the sun 378 how tall is the tree? Round final answer t0 the nearest tenth;



Answers

A pole leans away from the sun at an angle of 7° to the vertical, as shown in Figure 8.28. When the elevation of the sun is 55°, the pole casts a shadow 42 feet long on the level ground. How long is the pole? Round the answer to the nearest tenth.

Hi. We're looking at question seven, which asked, um to find the Wendy are They asked us to find the height of the flagpole to the nearest foot, so the severe H for height of the flag Buller you could call attacks. It doesn't matter. And it tells us the angle of elevation is 37 degrees and that the life will cast a shadow. There's 24.2 feet long, which is already labeled on my diagram. And so we're going to be able to find that height using tricking electric ratios and so and looking at the angle of elevation in this case because our horizontal is here and it's going up, so that would be an angle of elevation. And since this is our angle, we know that our high pot news is across from the right angle. Opposite is across from the angle, and adjacent is next to the angle s. Oh, that's for our trig functions. And so we need to decide which trig function is going to involve the opposite, because we have that as a tch and adjacent because we have that is 24.2, and if you remember, it's the tangent uses opposite over adjacent, and so the tangent and re always need an angle. So the tangent of the angle, which is 37 degrees, is equal to the opposite, which is a TSH, which is what we're looking for, and over the adjacent, which is 24.2. And then I like to suggest the students that if they put the trade function over one, then it makes it look like a proportion with you're more used to solving. So then we can just cross multiply in one times ages h and then you take 24.2 times the chanting of 37. Be careful that your calculator is in degrees, and that radiance is that will give you the wrong answer. And so when we calculate that H turns out to be 18 quite 236 feet. And if you don't get that answer, there's a good chance your calculators in radiance instead of degrees, and they want it to the nearest foot. So we need to round it appropriately, so the height is 18 feet

We are trying to figure this thehyperfix A poll based upon the following conditions. The poll actually has a seven degree lean to it and its shadow is 42 feet upon the ground when the angle of elevation to the sun is 55 degrees and the in the book has given us a drawing for that. Now we are going to use the law of science. But we are trying to figure out this length right here. I'm actually gonna call that a since its opposite angle capital way. Well, I don't know enough to use the law off signs yet, but I do know that if the pull was straight up and down, it would be perpendicular with the ground, or it would make a 90 degree angle. So if this part of the angle here is a 70 degree, seven degree lean in, that means that the angle here is going to be 83 degrees. Therefore, the angle at the top since we know a triangle was 180 degrees. When we add, the three interior angles together can be found by subtracting 55 degrees and 83 degrees. That would be a total of 42 degrees. So I'm going to say that the side of the bottom is C. It's opposite angle See, which is 42 degrees now. I'm going to use the law of signs comparing A's to seize a over sign Capital A equals C over Sign Capital C, which means a over the sign of 55 degrees equals 42 over Sign 42. And if I multiply the sign 55 that I have a by itself, so 42 times the sign of 55 degrees, divided by the sine of 42 degrees. Now remember, answer is going to be in feet, and our answer will be 51.4 feet.

Okay, So in this question, were given a 96 foot tree that casts a 120 foot shadow. So let's just say that the sun is like, right up here, and we need to find the angle of elevation to the sun. Well, basically, this would be the ankle right down here, which is the angle of elevation to the sun. So basically, find this angle, we're gonna have to use the tangent, the inverse tangent. So 10 inverse tangent of And since tan would be 96 over 1 20 would be inverse tangent of 96 over 1 20 And from here we would just use a calculator. And our answer is gonna be when we plug this into the calculator. 38 0.6 six degrees.

So a 96 foot tree casts a shadow that is 120 feet long. So we have a height of 96 lengthier of 120 feet. So we're being asked about the angle of elevation, which is they die here. In this case, we have the opposite and the adjacent sides of Fada. So this case, we use tangent. So Tangent Veda is 96 over 100 and 20. So from here on, we use 10 universe, so 10 in verse 96 divided by 1 20 that is equal to 38.7 degrees. And that's the angle of elevation off the sun.


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