what is the exact fractional value for the tangent of 15 degrees?

Answer 1

The tangent of 15 degrees = 2 - 3^0.5

Answer 2

Here's an easy way to get this that does not require remembering any trignometric identities:

Start with a 15-75-90 triangle ABC, where A is the vertex at the 15° angle, B the vertex at the 75° angle, and C the vertex at the right angle.

Find the point D on side AC such that AD = BD. Then, since ABD is isosceles, angle DBA = angle DAB = 15°. Therefore, angle CBD is 60°, and triangle BCD is a 30-60-90 triangle.

Knowing BCD is 30-60-90, let BC = 1. Then CD = √3, and BD = 2. Since BD = AD, AD = 2 also. Therefore, tan(15°) = BC/AC = BC/(AD + DC) = 1/(2 + √3). You can rationalize the denominator by multiplying top and bottom by 2 - √3, giving you the alternative exact value of 2 - √3.

Answer 3

what is the exact fractional value for the tangent of 15 degrees?

tan 15° = tan (60° - 45°)
= (tan60° - tan45°)/(1 + tan60° * tan45°)

= (√3 - 1)/(1 + √3*1)

= (√3 - 1)/(√3 + 1) * (√3 - 1)/(√3 - 1) (to rationalise the denominator)

= (4 - 2√3)/2

= 2 - √3 (exactly)

Answer 4

I don't know the exact fractional value but the rounded value of tan15 is .2679.

Answer 5

tan(15)=tan(45-30 )=tan 45 - tan 30/1+tan45*tan30 .
=1-1/sqrt(3/1+1/sqrt(3)=sqrt(3)-1/)sqrt(3) +1)=0.732/2.732=0.268