[20 Questions] Trigonometry, Locus&Parabola, Polynomials + More! :( (3 Viewers)

[tacogym27101990]

heres the majority of question 16,
but i ran out of room for the last bit so someone else can do it
or ill do it later if i can be bothered

 

[lolokay]

@jetblack: does a height of 1.172m make sense, considering the person is 1.8m tall?

your answer is correct (I think) right up until you put it into the quadratic formula (should be 2a, not a² as your denominator)

 

[jet]

Lol. what a stupid mistake. Ill fix it now.

 

[jet]

I finished question 16.

Please, next time, post each question into a different thread.

 

[AkaiHanabi]

I know that this is an old thread, but the answer for question 3 can be solved in a pretty simple way. the diagram below is based off of jetblack2007's diagram. First you construct parallel lines from the top of the man's head, then prove that the angle of elevation from the top of his head is the same angle as the ones subtended to the end of his shadow. Find tan theta (should be 1.8/6.5) and tan(x) (should be 1.8/9.1)

Then, to find the height of the tower minus the height of the man (which I'll call y), tan(theta)=y/EG. But we know that tan(theta)=1.8/6.5, so rearrange everything and you get EG=6.5y/1.8. Similarly FG=9.1y/1.8.

Now, we use the cosine formula so: (9.1y/1.8)^2=12^2 + (6.5y/1.8)^2 - 2*12*6.5y/1.8*cos120. Rearrange this to get a quadratic, then use the quadratic formula to find y. I found it to be 11.006 (3DP), then add 1.8 to find the total height, which I found to be 12.806.