Geometry: An Interactive Journey to Mastery

Solutions

5. ,IFRV x WKHQWKHSRLQWRQWKHXQLWFLUFOHPXVWEHGLUHFWO\RYHUKHDGRUGLUHFWO\EHORZ:HKDYH
   x ƒRUíƒRUƒRUíƒRUƒRUíƒDQGVRRQ


6. %\WKH3\WKDJRUHDQWKHRUHP VLQ xx^22  FRV 6R FRV x^2    ^2 VR
   FRV x |RUí


7. 6HHFigure S.16.1


8. 7KHSRLQWRQWKHXQLWFLUFOHPXVWEHLQWKHWKLUGTXDGUDQWVRƒxƒͼ௘RUƒxƒ
   RUíƒxíƒDQGVRRQ௘ͽ


9. )URPWKHVNHWFKLQFigure S.16.2LWLVFOHDUWKDWDSRLQW
   DWDQJOHRIHOHYDWLRQƒLVKLJKHUWKDQDSRLQWDWDQJOHRI
   HOHYDWLRQƒ
   7KXVVLQ ƒ VLQ ƒ !


10. )URPWKHWULDQJOHRQWKHOHIWLQFigure S.16.3LWLVFOHDU
    WKDWFRV ƒ VLQ ƒ   
    $QGLWLVDOVRFOHDUIURPWKHVNHWFKWKDW
    VLQ ƒ VLQ ƒ  
    7KXVVLQ ƒ LVODUJHUWKDQFRV ƒ 

í 



í

í 

yx cos

Figure S.16.1

50° 65°

Figure S.16.2

80° 80°

Figure S.16.3