Trigonometry Short Questions (Question 4 - 6)


Question 4:

In the diagram above, WZY  is a straight line.  XYZ= 90 o , XWZ= 30 o and WZ = XZ = 30 cm. Find the length of XY.

Solution:
WXZ=XWZ= 30 o XZY= 30 o + 30 o = 60 o sinXZY= XY XZ sin 60 o = XY 30 XY=sin 60 o ×30 XY=25.98cm


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:
5SR=2PS PS= 5 2 SR PS= 5 2 ( 6 ) PS=15 cm cosα= PQ PS cosα= 12 15 = 3 5 In  PQS, using Pythagoras' Theorem, QS= P S 2 P Q 2 QS= 15 2 12 2 =9 cm tanβ=tanPSQ Since  90 <β< 180 (in quadrant II), tanβ is negative tanβ= PQ QS tanβ= 12 9 = 4 3


Question 6:

In the diagram above, ADC is a straight line, if  sinq= 3 5  and tanp= 1 2 . Find the distance of AC.

Solution:
Given sinq= BD AB = 3 5 BD 30 = 3 5 BD= 3 5 ×30 BD=18 cm In  ABD, using Pythagoras' Theorem, AD= A B 2 B D 2 AD= 30 2 18 2 =24 cm Given tan p= BD DC = 1 2 18 DC = 1 2 DC=36 cm Hence, distance of AC=24+36=60 cm.