Question

construct angle of measure 22.5 degree by bisecting an angle of 45 degrees Hence find the value of tan 22.5 degrees ​

Answer 1

Answer:

Tan(22.5°) = 31 / 75

Step-by-step explanation:

we are draw the right angle triangle ΔABC with angle 45 degree on vertex B and C and then draw the bisector of angle C which is 22.5 degree

we know that

Tan(Ф) = Perpendicular / Base

And see in the figure the new triangle made by the bisecting the angle 45° is ΔADC

See in the ΔADC

The perpendicular = AD = 1.24

The Base = AC = 3

And

Tan(Ф) = Perpendicular / Base

Tan(22.5°) = AD / AC = 1.24 / 3 = 124 / 300 = 62 / 150 = 31 / 75

Thus

Tan(22.5°) = 31 / 75