A quadrilateral ABCD is divided into three triangular plots. BE = 100m, CD = 80m, ∠ABE = 30°, ∠ACE = 45°, ∠ACD = 100°. Find the length of AE.

Here is the solution to question 43 from the image you sent:

43. The figure below represents a quadrilateral piece of land ABCD divided into three triangular plots. The lengths BE and CD are 100m and 80m respectively. Angle ABE = 30°, angle ACE = 45° and angle ACD = 100°.

Assumptions: Based on the diagram and typical geometry problems, we assume that AE is perpendicular to BC, meaning $\angle AEB = 90^\circ$ and $\angle AEC = 90^\circ$.

a) Find to 4 significant figures:

• i) The length of AE.

  Step 1: Use trigonometry