The worth of tan (15°) is 0.26794919243. Tangent (tan) is one of the features of Trigonometry that encounters the relationships in between the angles and sides that a right-angled triangle. Therefore in short, we deserve to say that measuring a triangle (specifically right-angled triangle) is trigonometry. A right-angled triangle is a triangle having one the its interior angles as 90 degrees. Thus, in that case, the 3 sides of the triangle deserve to be called as:

Hypotenuse: The longest next of the triangle which is opposite to 90 degrees.

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Perpendicular (opposite): the is the side opposite come the unknown edge and perpendicular come the base (that is, the angle in between base and also perpendicular is 90 degrees).

Base (adjacent): it is the side on i m sorry triangle rests and it likewise contains both the angles (90 degrees and unknown edge .

If the unknown edge is 15 degrees then we can find the value of tan 15 degrees.

The most typically used trigonometric duty is sine, cos, and also tan. The end of which, only sin and also cos space the basic while the rest have the right to be acquired from sin and also cos.

As discussed above, tan is also derived native sin and also cos. The is,

< an left( heta ight) = fracOppositeAdjacent>

Therefore,

< an left( heta ight) = fracOppositeAdjacent>

Now, if the worth of is 15 degrees, that method one of the angle of a right-angled triangle is 15 degrees then us can discover the worth of tan 15 by placing the size of an opposite and adjacent side in the formula. Let us learn how to uncover the worth of the tangent of any type of angle.

Finding the Tangent

Let united state take an example of the right-angled triangle provided below. We deserve to see two unknown angles of less than 90 degrees (A and also B). If we take into consideration angle A as the unknown edge then

side measuring 5 will be hypotenuse, next measuring 3 will certainly be base, next measuring 4 will be perpendicular. Base and also Perpendicular will reverse if us take edge B as .

So according to the formula that tan that is,

< an left( heta ight) = fracOppositeAdjacent>

We deserve to say the the tangent of angle B is the proportion of next measuring 3 over the side measuring 4 or (3/4=0.75) and the tangent of angle A, is the ratio of next measuring 4 over the side measuring 3 or (4/3=1.33).

Similarly, us can uncover the worth of tan 15, if among the unknown angles of a right-angled triangle is 90 degrees. The approximate value of tan 15° would be 0.269.

Finding tan 15 value without utilizing sides:

Let united state take a best angle triangle having 15 levels as one of its angles. So, if in a right-angled triangle two angles space 90 and also 15 levels respectively, climate the 3rd angle have to be:

180 - (90 + 15) = 75 degrees. The size of the basic is x, perpendicular is y and hypotenuse is z.

To uncover tan 15 level value we have the right to represent 15 together 45 - 30.

tan(15°) = tan(45°-30°)

According to the formula of tan(A - B):

tan(A - B) = (tanA - tanB) /(1 + tan A tan B)

⇒tan(45°-30°) = (tan45°- tan30°)/(1+tan45°tan30°)

= 1- (1/√3) / 1+(1*1/√3)

∴ tan (15°) = (√3 - 1) / (√3 + 1)

tan (15°) = 2 - √3

On simplification, we acquire 0.26794919243.

Therefore,

Finding the worth of Tan 15 degrees using Sin and also Cos

Let us take a right angle triangle having actually 15 levels as among its angles. If the value of sin 15 and also cos 15 is given then us can discover the worth of tan 15.

According come the Formula,

< an heta = fracsin left( heta ight)cos left( heta ight)>

< herefore an left( 15^o ight) = fracsin left( 45 - 30 ight)^ocos left( 45 - 30 ight)^o>

Trigonometry formulas says that,

sin(A – B) = sin A cos B – cos A sin B and

cos (A – B) = cos A cos B + sin A sin B

Therefore,

< an left( 15^o ight) = fracleft( sin 45^ocos 30^o - cos 45^osin 30^o ight)^oleft( cos 45^ocos 30^o + sin 45^osin 30^o ight)>

On putting the worths of sin 30°, sin 45°, cos 30° and also cos 45°, us get,

tan (15°)= (1/√2.√3/2 – 1/√2.½) / (1/√2.√3/2 + 1/√2.½)

tan 15° = √3 – 1/ √3 + 1

∴ tan (15°) = (√3 - 1) / (√3 + 1)

tan (15°) = 2 - √3

On simplification, we obtain 0.26794919243.

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Therefore,

The worth of tan (15°) is 0.26794919243 |

Using the Tangent to find a missing Side

The next of the right-angled triangle utilizing tan can be discovered out by put the worths in the formula. Because that example: A right-angled triangle with among the angles as 66 degrees. If the size of the perpendicular is provided then the length of the base can be uncovered out. Let us take base together x.