Why is the tangent of 45 degrees equal 1?

Question

It is for school and I need it quick. Please don't be mean and lie.

Answer 1

In a 45-45-90 right triangle, the lengths of the legs are the same.

tan 45 = opposite leg / adjacent leg

Since the opposite leg and the adjacente leg are equal, then opp / adj = 1

Answer 2

Tangent Of 45 Degree Angle

Answer 3

Tangent is defined as the ratio of the opposite side to the adjacent side of a unit triangle.

In a 45°-45°-90° unit triangle, both sides are 1 and the hypotenuse (from Pythagorean theorem) is the square root of 1^2+1^2 or the square root of 2.

Given the definition above, the tangent of the 45° corner is a ratio of 1 over 1 or just plain 1.

Good Luck!

Answer 4

Remember that in a right triangle, the tangent of an angle is the "opposite over adjacent". When you have a 45 degree angle in a right triangle, this means you have a 45-45-90 triangle. This is also an isosceles triangle. So the side opposite of one of the 45 degree angles is the same length as the adjacent side. Thus tan(45) = (some number) / (the same number) = 1.

Answer 5

iyiogren provided the circular trig solution.

In plane trig, the formula for the tangent of an angle is simply the length of the opposite side over the length of the adjacent side.

Since the opposite is equal to the adjacent, the result is 1

(no I am not going to try to draw an isosceles right triangle with only text characters)

Answer 6

sum of 3 angles in a triangle is 180
one angle 90..
there fore the sum of the other 2 angles is 90
so if 1 angle is 45...then the other angle is 90-45 = 45..
there fore as angles r equal..their sides r equal..
tan theta = opposite side/ adjacent side
there for if theta is 45 the 2 sides r equal, they get cancelled
therefor tan 45 =1;

hope it helped..

Answer 7

tan 45 = sin 45 /cos 45 ,
but sin 45 = cos 45
then tan 45 =1

Answer 8

This Site Might Help You.

RE:
Why is the tangent of 45 degrees equal 1?
It is for school and I need it quick. Please don't be mean and lie.

Answer 9

because tan(x)= sin(x) / cos(x)

and the values of sin(x) and cos(x) are equal for 45 degrees (when x = pi / 4)

sin(45 degrees)= sin(pi/4)=cos(45 degrees) = cos(pi/4) = sqrt(2) / 2

so tan(45 degrees)= sin (pi/4) / cos(pi/4) = sqrt(2) / 2 / sqrt(2) / 2 = 1


can be proved using the Pythagorean Theorem, see
http://en.wikipedia.org/wiki/Trigonometric_function#Computation

Answer 10

a Right triangle with equal sides is 45 degrees if the run is one the rise is one. what level of explanation do you need.?