Trigonometry Short Questions (Question 4 – 6)


Question 4:

In the diagram above, WZY  is a straight line.  X Y Z = 90 o , X W Z = 30 o and WZ = XZ = 30 cm. Find the length of XY.

Solution:
W X Z = X W Z = 30 o X Z Y = 30 o + 30 o = 60 o sin X Z Y = X Y X Z sin 60 o = X Y 30 X Y = sin 60 o × 30 X Y = 25.98 c m



Question 5:

In the diagram above, PQS is a right angle triangle. Given that SR = 6cm, PQ = 12 cm and 5SR = 2PS. Find the value of cos α and tan β.

Solution:
5 S R = 2 P S P S = 5 2 S R P S = 5 2 ( 6 ) P S = 15 c m cos α = P Q P S cos α = 12 15 = 3 5 In P Q S , using Pythagoras’ Theorem, Q S = P S 2 P Q 2 Q S = 15 2 12 2 = 9 c m tan β = tan P S Q Since 90 < β < 180 ( in quadrant II), tan β is negative tan β = P Q Q S tan β = 12 9 = 4 3



Question 6:

In the diagram above, ADC is a straight line, if  sin q = 3 5 and tan p = 1 2 . Find the distance of AC.

Solution:
Given sin q = B D A B = 3 5 B D 30 = 3 5 B D = 3 5 × 30 B D = 18 c m In A B D , using Pythagoras’ Theorem, A D = A B 2 B D 2 A D = 30 2 18 2 = 24 c m Given tan p = B D D C = 1 2 18 D C = 1 2 D C = 36 c m Hence, distance of A C = 24 + 36 = 60 c m .

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