How do I determine an angle in a right triangle if I know all of the leg lengths?

Answer 1

If it's a Right Angle then the angle is 90 degrees, always.

For the other two angles, try the Pythagorean theorem.

A squared plus B squared equals C squared.

A and B are the two shorter sides, C is the long side (hypotenuse)

This wont give you the angles, but it will give the length of the other sides. Without additional information it is difficult to determine the angles.

Answer 2

Well if you have a right triangle, obviously one of the angles is 90 degrees. Then if two of the leg lengths are equal, then the other angles are both 45 degrees.

Answer 3

Given a right triangle, you need to use the trick of SOH-CAH-TOA:

sin(angle) = opposite side / hypotenuse

cos(angle) = adjacent side / hypotenuse

tan(angle) = opposite side / adjacent side

So given say a 3 - 4 - 5 right triangle with the angle being the angle of elevation, and 3 being the length of the side opposite the angle, 4 being the length of the side adjacent to the angle, and 5 being the length of the hypotenuse, we can find the angle using any of the parts of SOH - CAH - TOA.

sin(angle) = 3/5 First check on your calculator to make sure you are in degrees, then you would hit the 2nd button on your calculator, then the sin button, then 3/5 and you should get an angle in degrees. In our case it is appx 36.9 degrees.

cos(angle) = 4/5 Same procedure except you would hit the 2nd button, then the cos button, then 4/5 to get the same angle measurement of appx 36.9 degrees

tan(angle) = 3/4 Same procedure except you would hit the 2nd button, then the tan button, then 3/4 to get the same angle measurement of appx 36.9 degrees

Answer 4

I drew your triangle on paper and denoted the ninety degree attitude as C Then I marked the 87 degree attitude A and the three degree attitude B The length of the leg between A and C is 4 ft. This shall we me set up the equation Tan ( 87) = Opp / 4 ft subsequently 4' * Tan ( 87) = Opp = the leg between B and C this may grant you with a commence!

Answer 5

Let the two sides that form a right angle be called a and b.

Let the hypotenuse be called h.

The angle between a and b is 90 degrees since it is a right triangle.

The angle between a and h can be found from the trigonometric relationship:
a / h = cosine(angle)

So, the angle = inverse cosine of (a/h)

Answer 6

Only one angle of the triangle would be 90 degrees and you can't tell what the others are simply by the length of the legs.

Answer 7

Hi:

It is a right triangle if the square of longest leg equals the sum of the squares of the other two legs: then and only then is it a right triangle.

This is the definition of a right triangle as stated in my Geometry book

Answer 8

sine of an angle in a right triangle=the side opposite divided by the hypotenuse.
if C is the hypotenuse, then:

a=arcsin(A/C) and b=arcsin(B/C)
where A & B are the sides opposite angles a & b respectively.

Answer 9

If you know trigonometry:

sin (angle) = Length[opposite side to angle] / Length [hypotenuse].

Once you have the sine value you can get the angle from a trig table or your calculator.

Answer 10

at least one of the angles in a right triangle are always the same. the sum of all 3 angles in a triangle must add up to 180 degrees. a right triangle, by definition has 1 angle measuring 90 degrees.

if what you're thinking of is pythagorus' theorem then it's;

"In a right-angled triangle, the square on the hypotenuse, is the sum of the squares on the other two sides." (theorem discovered in 6th century bc, in greece)

here's a handy link that i looked up for you:
http://www.mathsisfun.com/right_angle_triangle.html