Question

Write the value of sin 30°and tan 60°​

Answer 1

Answer:

the value of sin 30 and tan 60 are

Step-by-step explanation:

1/2 and root3

Answer 2

The value of Sin 30° is 1/2 or 0.5.

Value of tan 60° is √3

Given,

Sin 30 degrees

Tan 60 degrees

To find,

Value of 30 degrees

Value of 60 degrees

Solution,

Let's assume a triangle ABC.

AB=2a, such that half of each side is A.

To find the value of sin 30 degree, we will use the formula,  

Sinϴ = Perpendicular/ Hypotenuse.            

Sin 30° = BD/AB =  a/2a = 12 

Thus, the value of Sin 30 degrees is 1/2 or 0.5.

Similarly,

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 find

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=√3

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