Question

ABCD is a square of length 60 cm E is a point inside the square such that angle EBC=angleECB=15 degree,Find the length of AE in cm.​

Answer 1

ABCD is a square of side 10cm. E is inside the square such that DE = 8cm and angle ECB = 40 degrees. Angle DEC is obtuse. Find the area of the triangle AEB.

Draw a line NEM parallel to BC and DA, N being on AB and M on DC.

<ECD = 90-<ECB = 90–40 = 50 deg.

In triangle EDC, DE/sin ECD = CD/<DEC, or

8/sin ECD = 10/sin DEC, or

8/sin 50 = 10/sin DEC, or

sin DEC = 10*sin 50/8 = 0.95755553. <DEC = arcsin 0.95755553 = 73.24685774 deg.

Since <DEC is obtuse its value = 180 - 73.24685774 = 106.7531423 deg.