What the fuck? The video shows a really, really complicated way to solve this problem. The guy resorts to trigonometry, but I solved this with simple geometry.
Try the problem out, then see my answer in the comments.
Wednesday, June 07, 2023
1 comment:
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Given the diagram (look at the video to see the lettering), we know segment DC = 3 + 9, which is 12, so AB must also equal 12.
ReplyDeleteBecause segment AF hits segment EB at EB's midpoint, we know that point F sits 1.5 units away from both horizontal sides of rectangle ABCD. F is also equidistant between points E and C. Draw a line segment upwards from F to the top of the rectangle and label that point of intersection G. Now you know that EG and GC are both 4.5 units (half of 9).
Draw a line segment straight down from point E to the bottom of the rectangle. Label that bottom intersection point H. Segment AH = 3 units.
Draw a line segment straight down from point F, stopping at the bottom of the rectangle. Label that intersection point I.
You now have a new triangle, AIF. If EG measures 4.5 units, then so does HI.
We now have the measurements for two out of three sides of triangle AIF. Segment AI must measure 3 + 4.5 = 7.5 units, and segment FI measures 1.5 units (see above, second paragraph). At this point, to solve for AF, just use Pythagoras.
7.5^2 + 1.5^2 = x^2
x^2 = 58.5
x = approx. 7.649 units.
QED.