A camera is mounted on a tripod 4 feet high at a distance of 10 feet from George
ID: 3097067 • Letter: A
Question
A camera is mounted on a tripod 4 feet high at a distance of 10 feet from George, who is 6 feet tall.If the camera lens has angles of depression and elevation of 20 degrees, will George's feet and head be seen by the lens?
If not how far back will the camera need to be moved to include George's feet and head? not sure if 4tan(90-20) would work out? need some help please
If not how far back will the camera need to be moved to include George's feet and head? not sure if 4tan(90-20) would work out? need some help please
Explanation / Answer
I would do this problem with sin rather than tangent. And i would do this by drawing two separate trangles. So first, i drew ONE triangle that's on TOP. Like, the shorter leg is 2 (since camera is 4 and he is 6 feet, 6-4=2). You know angle of elevation is 20. Then u use the sin theorem. Sin a/A=sin b/B assume a is 20, A is the number you want to find. b is 70 cuz (triangle has 180 degrees in total, one is 90 the right angle, another is 20, then 70 is left). B is given, which is 10 feet. (distane between camera and person) Plug it in solve for A you get 3.64 feet. From here you know that you do see the head, BUT you can't see the feet. Since the camera is 4 feet tall, and you can only see 3.64 feet up and down from that height (4feet). So u can only see in between 7.64feet and 0.36 feet. Your feet is at 0 feet btw. So you can't see the feet. You know u can see the head already so ignore the top triangle, and just use the bottom, where the shorter leg is 4. Now use the same equation Sin(a)/A=sin(b)/B but in this case, B (the distacne between camera and person) is the variable or the one you want to find. and A is constant which is 4. Since you want to see 4 feets or more. Then plug it in and solve for A oh btw, the angles are stillt eh same a is 20 degrees and b is 70 degrees. you get B=10.98feet. So that's how far back the camera need to be moved. Or 0.98 feets. Since the question asks "how far back" so im assuming how much more feet do u have to move to be able to see the feet.
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