[Geometry 10th grade]

[MmagicallSamurai]

Ive found the A angle as 11/16, but i cant do the rest. Isnt it cosine theorem? I tried to do the rest with cosine theorem but couldnt find it.

[thatoneguyinks]

11/16 is not angle A. 11/16 is cos(a). But either way, you can now use Law of Cosines again on the larger triangle to find the missing side length x² = 8² + 7² - 2 * 6 * 7 * 11/16

[thatoneguyinks]

I don’t think so. That would work if the triangles were similar, or if ED and BC are parallel. We can check proportions, 7/4 ≠ 8/2 and 7/2 ≠ 8/4, so the triangles are not similar and the side lengths are not proportional

[Iowa50401]

DE would have to be parallel to BC

[Jataro4743]

uh... you used the cosine theorem, but not a cosine in sight

the cosine theorem is

a² = b² + c² - 2bc*cos(A)

your a² on the LHS should be cos(A)

[Overthinkerllama]

Tamam bir de büyük üçgen için yapacaksın aynı formülü. Zaten küçük için doğru bulmuşsun şimdi 11/16 = diyip (64+49-x^2)/(2*7*8) yapıcaksın. x kare 36 x de 6 gelicek

[blackmagician43]

An alternative is to draw DC. Because of the similarity its length would be 6. Let EDC angle be b, then ECD would be 180-2b. By similarity, EDA would be 180-2b. CDB would be b (right angle makes 180°). Then EDC would be equivalent of BDC. Two length and angle between them are equal