Question

На рисунке 17 DE=DK, угол 1= угол 2. Найдите EC, угол DCK и угол DKC, если KC =1,8 дм, угол DCE =45, угол DEC =115 рис 17 https://ru-static.z-dn.net/files/d4d/44b4857d9582bd65931a1afbf6e4e76c.gif

Answer 1

Т.к. DE = DK и ∠1 = ∠2, то треугольники ΔDEC = ΔDCK равны по двум сторонам и углу между ними.

Следовательно:
EC = KC = 1,8 дм;
∠DCK = ∠DCE = 45°;
∠DKC = ∠DEC = 115°

Answer 2

Solution for Finding EC, Angle DCK, and Angle DKC

Given: - DE = DK - Angle 1 = Angle 2 - KC = 1.8 dm - Angle DCE = 45° - Angle DEC = 115°

We need to find: 1. EC 2. Angle DCK 3. Angle DKC

Finding EC

To find EC, we can use the fact that DE = DK and the given information about angles.

We know that in a triangle, if two sides are equal, the angles opposite those sides are also equal. Therefore, Angle DCE = Angle DCK.

Given that Angle DCE = 45°, we can conclude that Angle DCK = 45°.

Now, we can use the fact that the sum of angles in a triangle is 180° to find Angle ECD: Angle ECD = 180° - Angle DCE - Angle DCK Angle ECD = 180° - 45° - 45° Angle ECD = 90°

So, we have found that Angle ECD = 90°.

Now, we can use the sine rule to find EC: EC = (DE * sin(DEC)) / sin(ECD) = (DK * sin(115°)) / sin(90°) = (DK * sin(115°))

Finding Angle DKC and Angle DCK

We already know that Angle DCK = 45°.

To find Angle DKC, we can use the fact that the sum of angles in a triangle is 180°: Angle DKC = 180° - Angle DCK - Angle KCD Angle DKC = 180° - 45° - 90° Angle DKC = 45°

So, we have found that Angle DKC = 45°.

Conclusion

1. EC = DK * sin(115°) 2. Angle DCK = 45° 3. Angle DKC = 45°

This is the solution for finding EC, Angle DCK, and Angle DKC based on the given information and calculations.