1 Use the diagram below to answer the question that follows. Calculate the length of BC. 3.2 If tan θ + 15 = 0 and θ ∈ [90, 270], with the aid of a diagram, determine: 3.2.1 sin θ + cos θ 3.2.2 1/cos θ. 3.3 In rectangle ABCD, AB = 3x and BC = 4x. Find the length of AC and BD in terms of x.

Question 3:

• 3.1 Calculate the length of BC.

Step 1: Identify the right-angled triangle $\triangle DCE$.
The diagram shows a right angle at C, meaning $\angle DCE = 90^\circ$.
We are given $DE = 17$ cm and $CE = 8$ cm.
Using the Pythagorean theorem ($a^2 + b^2 = c^2$) in $\triangle DCE$:

$$DC^2 + CE^2 = DE^2$$ $$DC^2 + 8^2 = 17^2$$ $$DC^2 + 64 = 289$$ $$DC^2 = 289 - 64$$ $$$$