Question

Construct a quadrilateral PQRS where PQ = 5.6 cm, angle Q = 80°, angle R = 95°, QR = 6.2 cm and RS = 9.2 cm. What is the measurement of PS?

Answer 1

`7.05` cm ( 2 .d.p.)

Explanation:

From diagram:

`PR`

Using Cosine Rule:

`(PR)^2=(PQ)^2+(QR)^2-2(PQ)(QR)cos(Q)`

`(PR)^2=(5.6)^2+(6.2)^2-2(5.6)(6.2)cos(80)=57.741870`

`->=>PR=sqrt(57.741870)=7.5988=7.60` ( 2 .d.p. )

`/_QRP`

`cos(QRP)=((PR)^2+(QR)^2-(PQ)^2)/(2(PR)(QR))`

`cos(QRP)=((7.6)^2+(6.2)^2-(5.6)^2)/(2(7.6)(6.2))=0.6880305603`

`QRP = cos^-1(cos(QRP)) = cos^-1(0.6880305603)=46.53^@`

( 2 .d.p.)

`/_PRS=95^@-46.53^@=48.47^@`

`PS`

`(PS)^2= (PR)^2+(RS)^2-2(PR)(RS)cos(48.47^@)`

`(PS)^2=(7.6)^2+(9.2)^2-2(7.6)(9.2)cos(48.47)=49.684386`

`PS=sqrt(49.68438661)=7.048715245=7.05` ( 2 .d.p.)