How do you find the lengths of the sides of a right angled triangle if you only know the angles?

Question

i have a right angled triangle with an angle of 120°, another of 60° and the other of obviously 90°, but i don't know how i would use trigonometry to find the lengths of the sides, or even if this is possible....

Answer 1

Ignoring the fact that the angles you've given don't add up to 180 degrees (and so this shape is not a triangle), it is only possible with this information to find ratios of sides to one another. They are linked by the Sine Rule:



(For a triangle with sides a,b,c, and the angles opposite them being A,B,C respectively)



sin(A) / a = sin(B) / b = sin(C) / c



You can see why you can't find the absolute lengths of the sides by imagining the triangle being enlarged. The angles all stay the same but the sides can vary arbitrarily

Answer 2

The length of the side adjacent to the 30 degree angle (one of the inside angles must be 30 because the angles inside a triangle add up to 180) is 1. The length of the side adjacent to the 60 degree angle is the square root of 3. And the hypotenuse length is 2. This triangle is just one that you need to memorize for your trig class along with the side lengths for a 45-45-90 degree triangle (which are 1-1-square root 2, respectively). These are called special right triangles and should just be memorized. Hope this helps :)

Answer 3

it isn't available to remedy for the dimensions of an aspect of a triangle if actually given the dimensions of both different aspects devoid of any angles. you ought to both have 2 aspects and an attitude, 2 angles and a million part, 3 angles, or all 3 aspects. If all you've are those 2 part lengths, you could't remedy it.

Answer 4

That's not a right angled triangle... it's not a triangle at all, since every triangle has one condition: the sum of the inner angles is 180°! This one would have 270°, therefore no triangle.

Answer 5

Ya, it is impossible... The only thing I can think of is similar triangles, or the special properties of the 30-60-90; the opposite sides are always x, x*(3^0.5), and 2x, respectively.

Answer 6

It is not possible Cu's sum of angles in a triangle is 180 and the sum of angles in the question is more than 180.

Answer 7

You can't. You have to know at least one of the lengths to determine the other 2.