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Question

If the sides of a right-angled triangle are in AP then what are the sines of the acute angles?  [2 MARKS]


Solution

Concept: 1 Mark
Application: 1 Mark

Let C=90 being greatest and B=90A.

The sides are a - d, a and a + d. 

(a+d)2=(ad)2+a2 (using Pythagoras theorem)



4ada2=0a=4d

Hence the sides are 3d, 4d, 5d.

sin A=BCAB=ada+d=3d5d=35

sin B=ACAB=aa+d=4d5d=45

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