Sunday, March 18, 2007

ch. 7 review

can anyone explain 35 to me? i think i set up my diagram wrong.

thanks

posted by Anonymous at 8:31 PM

1 Comments:

Blogger Casey Blue said...

for this problem i started by drawing a vertical line segment, and labeled it as the building (448 ft.). I then drew a line segment starting at the top of the 448ft segment and slanting to the right and upward. At the end of this segment, I labeled the point as the airplane. I then connected the base of the vertical segment to the airplane. the book says the angle of elevation from the top of the building to the plane is 62degrees, so I drew a line perpendicular to the 448ft segment at the top of the building and called this "the horizontal." There are 62 degrees between this horizontal line and the segment slanting up toward the airplane. This means that when you make a triangle, the degree measure for that corner is 62 degrees PLUS an extra 90 (created by the building and the horizontal). The angle of elevation from the bottom of the building to the airplane is 65degrees, but this is outside the triangle! So when you redraw the triangle, the angle measure of this corner should be 25degrees (90-65). So now you have a triangle with one side of 448ft., one angle of 25degrees and another angle of 152 degrees. This means that the third angle is 3degrees (the angle opposite the 448 side). I used the law of sines to find the other two sides of the triangle, which give the answers for parts a and b. to find the height of the airplane, make a miniature right triangle out of the segment going from the top of the building to the plane, the horizontal that is perpendicular to the top of the building, and a line segment attaching these two. You already know the measure of the hypotenuse (you found it for part a), and you know that one angle is 62 degrees. To find the side opposite the angle (x), solve sin62=x/(hypotenuse). Add your value of x to 448 to find the height of the plane.

wow, that was complicated! I hope it wasn't too confusing. I must warn you that I re-tried the problem a couple times, and my values were always a little bit off from the book's values (well, about 300 ft. off for each answer). So... you might not want to rely on my method. But I'm think (...) this diagram set-up is correct, so I probably just screwed up my algebra or something. good luck!

8:55 PM  

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