The three angles of a triangle are in the ratio 1:2:3. Find the angles and classify the triangle.[3 marks]

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Solution

$G i v e n t h a t t h e r a t i o o f t h e a n g l e s o f t h e t r i a n g l e a r e 1 : 2 : 3 L e t t h e a n g l e s b e 1 x, 2 x, 3 x r e s p e c t i v e l y . [1 m a r k] A p p l y i n g a n g l e s u m p r o p e r t y ., 1 x + 2 x + 3 x = 180 ° 6 x = 180 ° x = 180 ° / 6 = 30 ° [1 m a r k] R e s p e c t i v e a n g l e s w i l l b e, 1 x = 30 ° 2 x = 2 x 30 ° = 60 ° 3 x = 3 x 30 ° = 90 ° T h e r e f o r e t h e r e q u i r e d a n g l e s a r e 30 °, 60 ° & 90 ° A s a l l t h e a n g l e s a r e d i f f e r e n t, w e c a n s a y t h a t t h e t r i a n g l e w i l l b e t h e S c a l e n e T r i a n g l e . [1 m a r k s]$

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