5

5. [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.

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

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

(This question continues on the following page)

(Question 5 continued)

A builder requires the lengths of the sides $[BA]$ and $[CE]$.
The builder has the following measurements:
$\angle ABC = \angle BCE = 90^\circ$, $DC = 50$ cm, $BC = 30$ cm, and $DF = 700$ cm.

(b) Find
(i) CE;

(ii) BA. [5]