4

4. [Maximum mark: 8]

The following diagram shows the cross section of the roof of a house. The cross section is symmetrical about the vertical line through points A and E. [Diagram shows a triangular roof structure with points A at the apex, E below A, and B, C, D, F along the base structure.]

The gradient of [BA] is $\frac{7}{12}$.

(a) Find the size of BÂE, expressing your answer in degrees. [3]

A builder requires the lengths of the sides [BA] and [CE].

The builder has the following measurements:
$A\hat{B}C = B\hat{C}E = 90^\circ$, $DC = 50\text{ cm}$, $BC = 30\text{ cm}$, and $DF = 700\text{ cm}$.

(b) Find
(i) CE;

(ii) BA. [5]