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:
A B 2 + 120 2 = 130 2 A B 2 = 130 2 120 2 AB= 130 2 120 2 AB= 2500 AB=50 m BC=12080=40 m tanθ= AB BC tanθ= 50 40 θ= 51 o 20



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)
A=( 1 2 ×3s× 4 2 t )π t 2 A=6stπ t 2

(ii)
A=6stπ t 2 A=6( 5 )( 7 )( 22 7 × 7 2 ) A=210154 A=56  cm 2


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