how do i find side ratios with only angles?

Question

I have a 27:63:90 triangle and I need to find the ratios of the sides, but i dont have any side lengths. How would I do this?

Answer 1

Hi,

Let the side opposite the 27° angle have a length of 1. Then to find the corresponding side length for the 63° angle's opposite side, say:
...................1
tan 27° = -----
....................x

................1
.5095 = -----
................x

........1
x = -------- = 1.9626 This is the 63° side length.
..._.5095

The hypotenuse would then be √(1² + 1.9626²) = 2.0268

So the ratio of the sides corresponding to 27:63:90 is 1:1.9626:2.0268. This could also be written as 1x:1.9626x:2.0268x to indicate this is the ratio of the sides, not necessarily the exact lengths.

I hope that helps!! :-)

Answer 2

This is a right triangle, so pick one of the two acute angles, and then use the definition of trigonometric functions:

sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent

And then you're done.

Answer 3

cos(63) = sin(27) = x , get x
then get , all sides in terms of x