The value of tan 60°

1.	The value of tan 60°
Answer» ong>Answer: The value of tan 60°=√3 Explanation: 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=AD According to AAS Congruency, Δ ABD ≅ Δ ACD From this, we can say BD = DC Let us TAKE, AB = BC =2a Then, BD= ½ (BC) =½ (2a) =a By using Pythagoras theorem, AB2 = AD2– BD2 AD2= AB2-BD2 AD2 =(2a)2 – a2 AD2 = 4a2-a2 AD2 = 3a2 Therefore, AD=a√3 Now in triangle ADB, Tan 600= AD/BD = a√3/a = √3 Therefore, tan 60 degrees exact value is given by, Tan 600=√3

Answer»

ong>Answer:

The value of tan 60°=√3

Explanation:

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=AD

According to AAS Congruency,

Δ ABD ≅ Δ ACD

From this, we can say

BD = DC

Let us TAKE, AB = BC =2a

Then, BD= ½ (BC) =½ (2a) =a

By using Pythagoras theorem,

AB2 = AD2– BD2

AD2= AB2-BD2

AD2 =(2a)2 – a2

AD2 = 4a2-a2

AD2 = 3a2

Therefore, AD=a√3

Now in triangle ADB,

Tan 600= AD/BD

= a√3/a = √3

Therefore, tan 60 degrees exact value is given by,

Tan 600=√3

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