# PT3 Mathematics 2017, Question 6

Question 6 (a):
In Diagram 6.1, PWVU is a straight line.

(i) Name the corresponding angle of ∠SWV.
(ii) State the value of ∠RVW.
(iii) Diagram 6.2 shows two parallel lines.

Based on Diagram 6.2, state two pairs of alternate angles.

Solution:
(i)TVU

(ii) 180o – 40o – 90o = 50o

(iii)
b and e
c and d

Question 6 (b):
Diagram 6.3 shows a lighthouse at the top of a cliff and two ships docked near the cliff.

Point B, C and D are aligned. Point A is vertically above point B. The distance between points C and titik D is 80 m.
Calculate the value of θ.

Solution:

Question 6 (c):
Diagram 6.4 shows a right angled triangle card. A circle with radius t cm has been cut from the card.

(i) Express the area of the remaining card, A, in terms of s and t.
(ii) Hence, calculate the value of A when s = 5 cm and t = 7 cm.

Solution:
(i)
$\begin{array}{l}A=\left(\frac{1}{\overline{)2}}×3s×{\overline{)4}}^{2}t\right)-\pi {t}^{2}\\ A=6st-\pi {t}^{2}\end{array}$

(ii)