trigonometry?

Question

If you got a right triangle, say a 30-60-90 triangle and you want to figure the Sin, Cos, and Tan of the right angle which leg do you label as the adjacent? My error is that the opp side is also the hypotenuse, therefore, there are two sides to select the adjacent but I don't know which one to use as adj.

On a 45-45-90 triangle, I don't have that problem because each leg is 1 while the hyp measures the square root of 2.

I'm sure to a mathematician this is non-issue. Where am I going wrong in my thinking?

thank you.

Answer 1

The hypotenuse is opposite the 90° angle

view from the 30° vertex is the opposite side

view from the 60° vertex is the adjacent side.

- - - - - - - - -s-

Answer 2

Let ABC be a right triangle with angle A = 60 angle B = 30 and angle C = 90.

Now if you look at angle A, one side of the angle is AB, the hypotenuse, and so the adjacent side must be AC, the other side of angle A. Clearly, BC is opposite angle A. The same applies to angle B. Clearly, AC is the side opposite and BC is the side adjacent.

When we are discussing angle C, we no longer refer to side adjacent. Instead we refer to the two legs of the right triangle. Except in the case of the isosceles right triangle. one leg is always larger than the other and both are smaller than the hypotenuse.

Answer 3

Your trouble comes from thinking of the hypotenuse as a leg.

There are two legs and a hypotenuse in a right triangle.

The hypotenuse is the side opposite the right angle. The other two sides are the legs.

The sin, cos and tan of 90 degrees don't need to be calculated. But, if you insist, since the adjecent side to the right angle is equivocal, using the value of zero will always give you the correct value for cos and tan. Sin = h/h = 1

Answer 4

That is a legitimate question.
Your only "error" is failing to realize that the labelling is all relative except for the hypotenuse, which is always the opposite side to the 90 degree angle. (opposite(in triangle world) means that it does not touch the angle at all.)
After the 90; you will have two other angles.
For either of the two angles the
non-hypotenuse side (or leg as you call it) is that specific angle's adjacent side.

Remember, there are two non-90-degree angles and one angle's opposite is the other angle's adjacent and vica-versa..

Answer 5

A vertex only has two sides that make it up. If one is the hypotenuse, then the other one is adjacent. If neither is the hypotenuse, then the angle you are referring to is the right angle.

Answer 6

think of it this way:
sin = y/r
cos = x/r
tan = y/x
r is the distance from the origin to (x,y)
you have a graph, and starting from the x-axis and going counterclockwise, you go 90 degrees so you land on the y-axis
since you are on the y-axis, the point would be (0,y) and the radius is the same as y
so
sin 90= y/r= y/y = 1
cos 90 = x/r = 0/y = 0
tan 90 = y/x = y/0 = undefined

Answer 7

the hypotenous is not the opposite look again in the problem u will find that the angle u r looking for is not the 90 angle.