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Please help :( In the figure below, triangle TED in rectangle TBCD is equilateral. If TB = 10, to the nearest hundredth, what is the length of ED?
Are you familiar with any trig?
hmm then again, you said geometry, so let me think of a way to do it without trig
no no, you can use a bit of trig if it is simple :)
Step 1) Label the length of ED x. So TE = x and TD = x as well since we're dealing with an equilateral triangle |dw:1338704023305:dw|
Step 2) Cut TD in half. Label the midpoint of TD point F and draw the segment EF |dw:1338704102241:dw|
The length of TF and FD are x/2 since we've cut TD = x in half
FE = TB, so FE = 10
So we have the following |dw:1338704182291:dw|
Since we have the right triangle EFD, we can say EF^2 + FD^2 = ED^2 but we know that EF = 10, FD = x/2 and ED = x, so... 10^2 + (x/2)^2 = x^2 100 + x^2/4 = x^2 400 + x^2 = 4x^2 400 = 4x^2 - x^2 400 = 3x^2 3x^2 = 400 x^2 = 400/3 x = sqrt(400/3) x = 20/sqrt(3) x = 20*sqrt(3)/3 So the exact length of ED is 20*sqrt(3)/3 units.
After that, use a calculator to get 20*sqrt(3)/3 = (20*1.73205)/3 = 34.641/3 = 11.547 Giving us that ED is approximately 11.547 units, which rounds to 11.55
thank you so much x) you really helped me x)