How do you find the sides of a right triangle is none of the sides are known?

Question

A right triangle has angles, 37, 90 and 53. How do you find the three sides of the triangle? (What trigonometric functions do I use?)

Answer 1

Then it can nnot be solved. You can have only parametric representations

say the hypotenous is x

other two sides will be

x sin 37 and x cos 37

so sides shall be

( x sin 37, x cos 37, x)

ALl the triangles are similar

Answer 2

The responses you've received so far are all basically correct.
However, the following information may be helpful to you.

The particular angles you mention are (to the nearest degree) the angles of the famous 3-4-5 right triangle.

As others have pointed out, any triangle of the same SHAPE will have those same angles. So the actual triangle could be 6-8-10, or 4.5-6-7.5, or 18-24-30. But all of these would be referred to as "3-4-5 right triangles," meaning that their sides are in those proportions.

Answer 3

There's no way to find the actual side lengths, but you can find them in relation to one another.

For example, let the hypoteneuse have length C.
The cosine of 37 is one of the sides (call it A) over C:
cos(37) = A/C ──►A = C*cos(37)
The sine of 37 is the other side (call it B) over C:
sin(37) = B/C ──► B = C*sin(37)

If you look at the angle 53 and you will find:
A = C*sin(53)
B = C*cos(53)

Answer 4

The minimum information needed to define a triangle is:
2 angles and
1 side length.

having all 3 angles is redundant and doesnt help you, because the triangle could be of any size, and the angles would be the same.

Answer 5

No can do. A triangle will be defined by any 3 of its 6 elements, except that one of the 3 elements has to be a side.

Answer 6

You can't find out the lenghts of the sides without at least one side. There are an infinite amount of triangles with those angles.

Answer 7

You must know at least one side. Otherwise, the given angles will only yield an infinite number of triangles.

Answer 8

The angles can give you the ratio of the sides but not the actual sides. You need at least one side so you have somewhere to start

Answer 9

By the sine rule
a/sinA = b/sinB = c/sinC

so a : b : c = sinA : sinB : sinC
= sin37° : sin90° : sin53°
≈0.602 : 1 : 0.800
≈ 6 : 10 : 8
= 3 : 5 : 4 (Of course we all know the famous 3.4.5 triangle, don't we!)

Answer 10

sin, cos, tan give you the ratios of the sides.
sin = opposite/hypotenuse, cos = adjacent/hypotenuse
tan = opposite/adjacent
with the ratios you can figure length of 2 sides, and pythagoras the third