In a right triangle ABC where AC is the Hypotenuse. Which one of the other lines (AB, BC) is the Opposite and which one is the Adjacent .. from the corner 90???
I mean if the angels are 45-45-90 and i want to count the Sin90 or Cos90 ... etc. It's easy to tell the H, O, and A lines from the corner 45 degree, but I get mixed up between the H and the O looking at it from the corner 90 degree.
Please help.
2006-12-24 19:35:17 · 13 answers · asked by khaled450 1 in Science & Mathematics ➔ Mathematics
In your right angled triangle ABC, you have told that AC is hypotenuse.
That will be always hypotenuse and is opposite to the 90 degree.
The adjacent and opposite sides are with respect to the other two angles only.
There is no adjacent or opposite to the 90 degree. It is because opposite of this 90 degree is always hypotenuse.
The sum of the other two angles is always 90 degree.
Let angle A be 30 degree. The side BC is opposite to 30 degree. We can find sin and cos of 30 degree.
If this angle is gradually increased from 30 degree, (keeping the angle B always at 90 degree) the maximum angle it can reach in this right angled triangle is 90 degree and the other angle will become 0 degree. (The triangle is now a mere straight line, B and C coincides)
Now you can find the value of sin 90 or cos 90 in this case. Remember the hypotenuse is the same which is opposite to the 90 degree (angle B).
Hence there is no adjacent or opposite to the 90 degree of the right angled triangle. The opposite side is always hypotenuse.
2006-12-25 00:45:48 · answer #1 · answered by Pearlsawme 7 · 0⤊ 0⤋
You really don't compute sin, cos, etc from the 90° angle. All the calculations assume you are at one of the other two corners, where the hypotenuse is one of the sides that comes to the angle.
If you were to construct a triangle to calculate the sin and cos of 90°, it would be a degenerate triangle with two 90° angles and one 0° angle. In that case one of the legs of the triangle would be the same length as the hypotenuse and the other would be of length zero. It would look like a line segment that doubled back on itself.
So from the second 90° angle:
sin 90° = opposite side/hypotenuse = 1 because the two sides are of equal length.
cos 90° = adjacent side/hypotenuse = 0 because the adjacent side has length zero.
As I said, it is a degenerate triangle.
If this explanation troubles you, think of it in terms of a limit. As the larger of the two acute angles approaches 90°, the smaller angle approaches 0°. As this happens, the length of the larger leg approaches the length of the hypotenuse and the length of the smaller approaches zero. And you will get the same result calculating sin and cos as before.
2006-12-24 19:52:12 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
Each leg is 7(sqrt(2))/2. There is a law of triangles that the length of the hypotenuse of a right triangle with congruent angles (your 45-45-90) is the length of one of the legs times the square root of 2. So, the leg is 7 divided by the square root of 2. This is 4.95. Why is the length of the hypotenuse always the square root of 2 times the length of the leg in a 45-45-90 triangle? Recall the ubiquitous: a^2 + b^2 = c^2 Since a = b, you have: a^2 + a^2 = c^2 2a^2 = c^2 sqrt(2) * a = c
2016-05-23 05:19:17 · answer #3 · answered by Anonymous · 0⤊ 0⤋
When calculating sin cos it doesnt matter which angle you take a s adjacent or opposites as long as you put the correct value of the relevent angle.In case of 45-45-90 both the sin and cos are same for the 45 value
The hypotaneuseis the opposite side if the 90 angle and in other triangles the longest side.
2006-12-24 20:20:40 · answer #4 · answered by Shahzadi 3 · 0⤊ 0⤋
The longest leg of the triangle is the hypotenuse. And the hypotenuse is ALWAYS the hypotenuse... it can never be the leg opposite or the leg adjacent - never!
So... if you were to put either of the points, (not the 90 deg. end), of the triangle in your eye, then one leg, (or side), projecting out from your eye would be the side adjacent and the other would be the hypotenuse and the one you'd be looking towards would be the side opposite - ALWAYS!
(It's pretty hard to describe this in writing without using a diagram!)
2006-12-24 19:46:01 · answer #5 · answered by love_2b_curious 6 · 1⤊ 0⤋
The Hypotenuse is the longest side.
The Hypotenuse is opposite the 90° angle
30 - 60 - 90 degree Triangle
The hypotenuse is the ray beginning at the vertex of the 30° angle and assending and terminating at the vertex of the 60° angle.
- - - - - - -s-
2006-12-25 02:44:22 · answer #6 · answered by SAMUEL D 7 · 0⤊ 0⤋
AB or BC is the opposite or adjacent is determined by the angle that it corresponds to. In a right angle triangle, if the angle ACB is the angle that you are looking for, the adjacent would be BC and opposite would be AB. Similarly for the other angle, it is a matter of where the angle is.
2006-12-24 22:00:05 · answer #7 · answered by PIPI B 4 · 0⤊ 0⤋
The hypotenuse is longer side of the right triangle.
2006-12-25 02:03:28 · answer #8 · answered by Anonymous · 0⤊ 0⤋
the side opposite the 90*
2006-12-24 19:37:22 · answer #9 · answered by raj 7 · 1⤊ 0⤋
In any right triangle, the hypotenuse is always the longest side .
2006-12-24 19:40:51 · answer #10 · answered by sahsjing 7 · 2⤊ 0⤋