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Value of tan 60 |
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Answer» To find the value of tan 60 degrees geometrically, consider an equilateral triangle ABC since each of an angle in an equilateral triangle is 600.Therefore, ∠A = ∠B = ∠C = 60°Draw a perpendicular line AD from A to BC.Now consider the triangle, ABD and ADC,We have, ∠ ADB = ∠ADC= 90° and∠ ABD = ∠ACD= 60°Therefore, AD=ADAccording to AAS Congruency,Δ ABD ≅ Δ ACDFrom this, we can sayBD = DCLet us take, AB = BC =2aThen, BD= ½ (BC) =½ (2a) =aBy using Pythagoras theorem,AB2 = AD2– BD2AD2= AB2-BD2AD2 =(2a)2 – a2AD2 = 4a2-a2AD2 = 3a2Therefore, AD=a√3Now in triangle ADB,Tan 600= AD/BD= a√3/a = √3Therefore, tan 60 degrees exact value is given by,Tan 600=√3 √3 Root 3 √3 √3 1.732=tan60 √3 is the value of tan60 √3 |
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