If I have a right angled tringle and I know the length of all three sides, how do I find the other angles ( other than the right angle). I know it involves arc cos/sin/tan but I can't remember exactly how it is arranged. Any help?
2007-05-04 10:19:35 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
For the unknown angle, let the sin (angle) = opposite side/hypotenuse (or cos = adjacent side/hypotenuse) - and you will get a numerical answer.
You get the angle itself by working out the inverse sin (or cos) of this value (you can use your calculator for that, or look it up in tables) - both sin and cos methods will give you the same answer, as you are using different sides to get there.
2007-05-04 10:30:10 · answer #1 · answered by billibette 3 · 0⤊ 1⤋
sin(angle) = opposite / hypotenuse
cos(angle) = adjacent / hypotenuse
angle = sin^-1(opposite / hypotenuse)
angle = cos^-1(adjancent/hypotenuse)
One of the angle is 90 degrees. There are 180 degrees in a triangle.
The law of cosines states:
c^2 = a^2 + b^2 - 2ab * cos (C)
Where a, b, and c are the length of the sides and C is the angle opposite the the side, c.
2007-05-04 10:27:55 · answer #2 · answered by the redcuber 6 · 1⤊ 1⤋
If you have the lengths of all three sides, and the right angle, all you need are the remaining two angles. All you really need to do is use trig to solve for one angle and subtract from 180 degrees to get the third angle. Here's one way to do it. Pick one of the two unknown angles. Determine what the opposite and adjacent sides are (we're going to use tan inverse). Tan x = opposite/adjacent. So, x = tan inverse (opposite/adjacent). Now that you have two of the three angles, sum the two and subtract the sum from 180 degrees to get the third unknown angle. Hope that helps :)
2007-05-04 10:27:47 · answer #3 · answered by Anonymous · 0⤊ 1⤋
Not neccessarily specific to right angled triangles, but you need the cosine rule:
a² = b² + c² - 2bc cos A
or
cos A = (b² + c² - a²) / 2bc
and then find A, by finding arccos of cosA ( cos-1 on the calculator)
2007-05-04 10:32:50 · answer #4 · answered by Blimey! 3 · 0⤊ 0⤋
You could also use the law of sines which states: sin(a)/A=sin(b)/B=sin(c)/C
where A, B and C are the length of the sides, and a, b, and c are the angles opposite to their respective sides (i.e. a is opposite A) then just pick any pair and the hypotenuse/90degree angle pair, and solve.
2007-05-04 10:31:41 · answer #5 · answered by Lazer Fazer 2 · 0⤊ 1⤋
Consider right angled triangle ABC right angled at B.
AB is vertical and CB is horizontal.
Tan C = AB/BC
Angle C can thus be found.
A = 90° - C
All angles are then known.
2007-05-04 10:34:05 · answer #6 · answered by Como 7 · 0⤊ 1⤋
cos: the leg next to the angle over the hypotenuse.
sin: the leg opposite of the angle over the hypotenuse.
2007-05-04 10:30:41 · answer #7 · answered by Amit Y 5 · 0⤊ 1⤋
Remember a triangles measurements of all three sides is 180 degrees. So 90 degress plus Opposite plus Hypothenus. should equal 180 degrees.
2007-05-04 10:26:33 · answer #8 · answered by StylishDude 3 · 0⤊ 2⤋
Memorize this: "SOH-CAH-TOA". Sine = Opposite over Hypotenuse. Cosine = Adjacent over Hypotenuse. And Tangent = Opposite over Adjacent.
2007-05-04 10:30:19 · answer #9 · answered by Anonymous · 0⤊ 1⤋