Question

Why would the tangent of 45 degrees always equal 1 ?

Answer 1

We would prove this with a right isosceles triangle. The diagram is shown below

Cosidering triangle ABC, if we take angle A as the reference angle,

opposite side = BC = 1

adjacent side = AB = 1

hypotenuse = AC

The tangent trigonometric ratio is expressed as

Tan # = opposite side/adjacent side

Thus,

Tan 45 = 1/1

Tan 45 = 1