How do you find the hypotenuse with only a leg and a degree?

It depends on the position of the 'leg' compared to the known angle.

If the 'leg' makes up one of the two sides of the angle, then the other side of the angle is the hypotenuse.

In this case the 'leg' would be referred to as the 'adjacent' side.

The side the doesn't form part of the angle is referred to as the 'opposite' side.

So using the trig. functions.

Sin(angle) = opposite / hypotenuse.

Then algebraically rearranging

hypotenuse = opposite / Sin(angle).

Similarly for 'Cos'.

Cos(angle) = adjacent/ hypotenuse

Hence

Hypotenuse = adjacent / Cos(angle)

So as an example

If the leg/opposite is 2 units. and the angle 30 degrees.

Then

hypotenuse = 2 / Sin(30).

On you calculator you should be find the Sin( 30) = 1/2 = 0.5

Substitute in

hypotenuse = 2 / 1/2 ( That is '2' divided by '1/2'), (Division of fractions).

hypotenuse = 2 X 2/1 = 4/1 = 4 units.

NB When using your calculator to find 'Sin' , 'Cos', and 'Tan' of angles, you will read out some 'horrible' decimal numbers.

NNB Do NOT use the TAN(gent) function to find hypotenuse. It is NOT part of the Tan ratio.

Here is an 'aide memoire' for the Trig . functions.

SOH , CAH, TOA. ( Said as 'soccatoa').

SOH = Sin(angle) = opposite/ hypotenuse = o/h

CAH = Cos(angle) = adjacent/hypotenuse = a/h

TOA = Tan(Angle) = opposite/adjacent = o/a